Basic Math Examples

$5 {(p - 2 q)}^{2} (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 1

Rewrite ${(p - 2 q)}^{2}$ as $(p - 2 q) (p - 2 q)$ .

$5 ((p - 2 q) (p - 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 2

Expand $(p - 2 q) (p - 2 q)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 (p (p - 2 q) - 2 q (p - 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 2.2

Apply the distributive property.

$5 (p \cdot p + p (- 2 q) - 2 q (p - 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 2.3

Apply the distributive property.

$5 (p \cdot p + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $p$ by $p$ .

$5 (p^{2} + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$5 (p^{2} - 2 p q - 2 q p - 2 q (- 2 q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$5 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q \cdot q) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.1.4

Multiply $q$ by $q$ by adding the exponents.

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Step 3.1.4.1

Move $q$ .

$5 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 (q \cdot q)) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.1.4.2

Multiply $q$ by $q$ .

$5 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.1.5

Multiply $- 2$ by $- 2$ .

$5 (p^{2} - 2 p q - 2 q p + 4 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.2

Subtract $2 q p$ from $- 2 p q$ .

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Step 3.2.1

Move $q$ .

$5 (p^{2} - 2 p q - 2 p q + 4 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 3.2.2

Subtract $2 p q$ from $- 2 p q$ .

$5 (p^{2} - 4 p q + 4 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 4

Apply the distributive property.

$(5 p^{2} + 5 (- 4 p q) + 5 (4 q^{2})) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 5

Simplify.

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Step 5.1

Multiply $- 4$ by $5$ .

$(5 p^{2} - 20 (p q) + 5 (4 q^{2})) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 5.2

Multiply $4$ by $5$ .

$(5 p^{2} - 20 (p q) + 20 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 6

Remove parentheses.

$(5 p^{2} - 20 p q + 20 q^{2}) (a + b) + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 7

Expand $(5 p^{2} - 20 p q + 20 q^{2}) (a + b)$ by multiplying each term in the first expression by each term in the second expression.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 {(p - 2 q)}^{2} (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 8

Rewrite ${(p - 2 q)}^{2}$ as $(p - 2 q) (p - 2 q)$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 ((p - 2 q) (p - 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 9

Expand $(p - 2 q) (p - 2 q)$ using the FOIL Method.

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Step 9.1

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p (p - 2 q) - 2 q (p - 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 9.2

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p \cdot p + p (- 2 q) - 2 q (p - 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 9.3

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p \cdot p + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10

Simplify and combine like terms.

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Step 10.1

Simplify each term.

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Step 10.1.1

Multiply $p$ by $p$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.1.2

Rewrite using the commutative property of multiplication.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 q p - 2 q (- 2 q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.1.3

Rewrite using the commutative property of multiplication.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q \cdot q) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.1.4

Multiply $q$ by $q$ by adding the exponents.

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Step 10.1.4.1

Move $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 (q \cdot q)) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.1.4.2

Multiply $q$ by $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.1.5

Multiply $- 2$ by $- 2$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 q p + 4 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.2

Subtract $2 q p$ from $- 2 p q$ .

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Step 10.2.1

Move $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 2 p q - 2 p q + 4 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 10.2.2

Subtract $2 p q$ from $- 2 p q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 (p^{2} - 4 p q + 4 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 11

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + (3 p^{2} + 3 (- 4 p q) + 3 (4 q^{2})) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 12

Simplify.

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Step 12.1

Multiply $- 4$ by $3$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + (3 p^{2} - 12 (p q) + 3 (4 q^{2})) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 12.2

Multiply $4$ by $3$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + (3 p^{2} - 12 (p q) + 12 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 13

Remove parentheses.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + (3 p^{2} - 12 p q + 12 q^{2}) (a + b) - 14 {(p - 2 q)}^{2} (a + b)$

Step 14

Expand $(3 p^{2} - 12 p q + 12 q^{2}) (a + b)$ by multiplying each term in the first expression by each term in the second expression.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 {(p - 2 q)}^{2} (a + b)$

Step 15

Rewrite ${(p - 2 q)}^{2}$ as $(p - 2 q) (p - 2 q)$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 ((p - 2 q) (p - 2 q)) (a + b)$

Step 16

Expand $(p - 2 q) (p - 2 q)$ using the FOIL Method.

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Step 16.1

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p (p - 2 q) - 2 q (p - 2 q)) (a + b)$

Step 16.2

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p \cdot p + p (- 2 q) - 2 q (p - 2 q)) (a + b)$

Step 16.3

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p \cdot p + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b)$

Step 17

Simplify and combine like terms.

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Step 17.1

Simplify each term.

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Step 17.1.1

Multiply $p$ by $p$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} + p (- 2 q) - 2 q p - 2 q (- 2 q)) (a + b)$

Step 17.1.2

Rewrite using the commutative property of multiplication.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 q p - 2 q (- 2 q)) (a + b)$

Step 17.1.3

Rewrite using the commutative property of multiplication.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q \cdot q) (a + b)$

Step 17.1.4

Multiply $q$ by $q$ by adding the exponents.

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Step 17.1.4.1

Move $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 (q \cdot q)) (a + b)$

Step 17.1.4.2

Multiply $q$ by $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q^{2}) (a + b)$

Step 17.1.5

Multiply $- 2$ by $- 2$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 q p + 4 q^{2}) (a + b)$

Step 17.2

Subtract $2 q p$ from $- 2 p q$ .

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Step 17.2.1

Move $q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 2 p q - 2 p q + 4 q^{2}) (a + b)$

Step 17.2.2

Subtract $2 p q$ from $- 2 p q$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 (p^{2} - 4 p q + 4 q^{2}) (a + b)$

Step 18

Apply the distributive property.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b + (- 14 p^{2} - 14 (- 4 p q) - 14 (4 q^{2})) (a + b)$

Step 19

Simplify.

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Step 19.1

Multiply $- 4$ by $- 14$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b + (- 14 p^{2} + 56 (p q) - 14 (4 q^{2})) (a + b)$

Step 19.2

Multiply $4$ by $- 14$ .

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b + (- 14 p^{2} + 56 (p q) - 56 q^{2}) (a + b)$

Step 20

Remove parentheses.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b + (- 14 p^{2} + 56 p q - 56 q^{2}) (a + b)$

Step 21

Expand $(- 14 p^{2} + 56 p q - 56 q^{2}) (a + b)$ by multiplying each term in the first expression by each term in the second expression.

$5 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} a + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 p^{2} a - 14 p^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 22

Add $5 p^{2} a$ and $3 p^{2} a$ .

$8 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 p^{2} a - 14 p^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 23

Subtract $14 p^{2} a$ from $8 p^{2} a$ .

$- 6 p^{2} a + 5 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b + 3 p^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 p^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 24

Add $5 p^{2} b$ and $3 p^{2} b$ .

$- 6 p^{2} a + 8 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b - 14 p^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 25

Subtract $14 p^{2} b$ from $8 p^{2} b$ .

$- 6 p^{2} a - 6 p^{2} b - 20 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b - 12 p q a - 12 p q b + 12 q^{2} a + 12 q^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 26

Subtract $12 p q a$ from $- 20 p q a$ .

$- 6 p^{2} a - 6 p^{2} b - 32 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b - 12 p q b + 12 q^{2} a + 12 q^{2} b + 56 p q a + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 27

Add $- 32 p q a$ and $56 p q a$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a - 20 p q b + 20 q^{2} a + 20 q^{2} b - 12 p q b + 12 q^{2} a + 12 q^{2} b + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 28

Subtract $12 p q b$ from $- 20 p q b$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a - 32 p q b + 20 q^{2} a + 20 q^{2} b + 12 q^{2} a + 12 q^{2} b + 56 p q b - 56 q^{2} a - 56 q^{2} b$

Step 29

Add $- 32 p q b$ and $56 p q b$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b + 20 q^{2} a + 20 q^{2} b + 12 q^{2} a + 12 q^{2} b - 56 q^{2} a - 56 q^{2} b$

Step 30

Add $20 q^{2} a$ and $12 q^{2} a$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b + 32 q^{2} a + 20 q^{2} b + 12 q^{2} b - 56 q^{2} a - 56 q^{2} b$

Step 31

Subtract $56 q^{2} a$ from $32 q^{2} a$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b - 24 q^{2} a + 20 q^{2} b + 12 q^{2} b - 56 q^{2} b$

Step 32

Add $20 q^{2} b$ and $12 q^{2} b$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b - 24 q^{2} a + 32 q^{2} b - 56 q^{2} b$

Step 33

Subtract $56 q^{2} b$ from $32 q^{2} b$ .

$- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b - 24 q^{2} a - 24 q^{2} b$

Step 34

Factor $6$ out of $- 6 p^{2} a - 6 p^{2} b + 24 p q a + 24 p q b - 24 q^{2} a - 24 q^{2} b$ .

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Step 34.1

Factor $6$ out of $- 6 p^{2} a$ .

$6 (- p^{2} a) - 6 p^{2} b + 24 p q a + 24 p q b - 24 q^{2} a - 24 q^{2} b$

Step 34.2

Factor $6$ out of $- 6 p^{2} b$ .

$6 (- p^{2} a) + 6 (- p^{2} b) + 24 p q a + 24 p q b - 24 q^{2} a - 24 q^{2} b$

Step 34.3

Factor $6$ out of $24 p q a$ .

$6 (- p^{2} a) + 6 (- p^{2} b) + 6 (4 p q a) + 24 p q b - 24 q^{2} a - 24 q^{2} b$

Step 34.4

Factor $6$ out of $24 p q b$ .

$6 (- p^{2} a) + 6 (- p^{2} b) + 6 (4 p q a) + 6 (4 p q b) - 24 q^{2} a - 24 q^{2} b$

Step 34.5

Factor $6$ out of $- 24 q^{2} a$ .

$6 (- p^{2} a) + 6 (- p^{2} b) + 6 (4 p q a) + 6 (4 p q b) + 6 (- 4 q^{2} a) - 24 q^{2} b$

Step 34.6

Factor $6$ out of $- 24 q^{2} b$ .

$6 (- p^{2} a) + 6 (- p^{2} b) + 6 (4 p q a) + 6 (4 p q b) + 6 (- 4 q^{2} a) + 6 (- 4 q^{2} b)$

Step 34.7

Factor $6$ out of $6 (- p^{2} a) + 6 (- p^{2} b)$ .

$6 (- p^{2} a - p^{2} b) + 6 (4 p q a) + 6 (4 p q b) + 6 (- 4 q^{2} a) + 6 (- 4 q^{2} b)$

Step 34.8

Factor $6$ out of $6 (- p^{2} a - p^{2} b) + 6 (4 p q a)$ .

$6 (- p^{2} a - p^{2} b + 4 p q a) + 6 (4 p q b) + 6 (- 4 q^{2} a) + 6 (- 4 q^{2} b)$

Step 34.9

Factor $6$ out of $6 (- p^{2} a - p^{2} b + 4 p q a) + 6 (4 p q b)$ .

$6 (- p^{2} a - p^{2} b + 4 p q a + 4 p q b) + 6 (- 4 q^{2} a) + 6 (- 4 q^{2} b)$

Step 34.10

Factor $6$ out of $6 (- p^{2} a - p^{2} b + 4 p q a + 4 p q b) + 6 (- 4 q^{2} a)$ .

$6 (- p^{2} a - p^{2} b + 4 p q a + 4 p q b - 4 q^{2} a) + 6 (- 4 q^{2} b)$

Step 34.11

Factor $6$ out of $6 (- p^{2} a - p^{2} b + 4 p q a + 4 p q b - 4 q^{2} a) + 6 (- 4 q^{2} b)$ .

$6 (- p^{2} a - p^{2} b + 4 p q a + 4 p q b - 4 q^{2} a - 4 q^{2} b)$