Basic Math Examples

$y (p - 2 q) (p - 2 q) + y (2 q - p) (2 p - p)$

Step 1

Factor $y$ out of $y (p - 2 q) (p - 2 q) + y (2 q - p) (2 p - p)$ .

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Step 1.1

Factor $y$ out of $y (p - 2 q) (p - 2 q)$ .

$y ((p - 2 q) (p - 2 q)) + y (2 q - p) (2 p - p)$

Step 1.2

Factor $y$ out of $y (2 q - p) (2 p - p)$ .

$y ((p - 2 q) (p - 2 q)) + y ((2 q - p) (2 p - p))$

Step 1.3

Factor $y$ out of $y ((p - 2 q) (p - 2 q)) + y ((2 q - p) (2 p - p))$ .

$y ((p - 2 q) (p - 2 q) + (2 q - p) (2 p - p))$

Step 2

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

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Step 2.1

Apply the distributive property.

$y (p (p - 2 q) - 2 q (p - 2 q) + (2 q - p) (2 p - p))$

Step 2.2

Apply the distributive property.

$y (p \cdot p + p (- 2 q) - 2 q (p - 2 q) + (2 q - p) (2 p - p))$

Step 2.3

Apply the distributive property.

$y (p \cdot p + p (- 2 q) - 2 q p - 2 q (- 2 q) + (2 q - p) (2 p - p))$

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 $p$ .

$y (p^{2} + p (- 2 q) - 2 q p - 2 q (- 2 q) + (2 q - p) (2 p - p))$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$y (p^{2} - 2 p q - 2 q p - 2 q (- 2 q) + (2 q - p) (2 p - p))$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$y (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q \cdot q + (2 q - p) (2 p - p))$

Step 3.1.4

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

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Step 3.1.4.1

Move $q$ .

$y (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 (q \cdot q) + (2 q - p) (2 p - p))$

Step 3.1.4.2

Multiply $q$ by $q$ .

$y (p^{2} - 2 p q - 2 q p - 2 \cdot - 2 q^{2} + (2 q - p) (2 p - p))$

Step 3.1.5

Multiply $- 2$ by $- 2$ .

$y (p^{2} - 2 p q - 2 q p + 4 q^{2} + (2 q - p) (2 p - p))$

Step 3.2

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

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Step 3.2.1

Move $q$ .

$y (p^{2} - 2 p q - 2 p q + 4 q^{2} + (2 q - p) (2 p - p))$

Step 3.2.2

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

$y (p^{2} - 4 p q + 4 q^{2} + (2 q - p) (2 p - p))$

Step 4

Subtract $p$ from $2 p$ .

$y (p^{2} - 4 p q + 4 q^{2} + (2 q - p) p)$

Step 5

Apply the distributive property.

$y (p^{2} - 4 p q + 4 q^{2} + 2 q p - p \cdot p)$

Step 6

Multiply $p$ by $p$ by adding the exponents.

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Step 6.1

Move $p$ .

$y (p^{2} - 4 p q + 4 q^{2} + 2 q p - (p \cdot p))$

Step 6.2

Multiply $p$ by $p$ .

$y (p^{2} - 4 p q + 4 q^{2} + 2 q p - p^{2})$

Step 7

Subtract $p^{2}$ from $p^{2}$ .

$y (- 4 p q + 4 q^{2} + 2 q p + 0)$

Step 8

Add $- 4 p q + 4 q^{2} + 2 q p$ and $0$ .

$y (- 4 p q + 4 q^{2} + 2 q p)$

Step 9

Add $- 4 p q$ and $2 q p$ .

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Step 9.1

Move $q$ .

$y (4 q^{2} - 4 p q + 2 p q)$

Step 9.2

Add $- 4 p q$ and $2 p q$ .

$y (4 q^{2} - 2 p q)$

Step 10

Factor.

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Step 10.1

Factor $2 q$ out of $4 q^{2} - 2 p q$ .

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Step 10.1.1

Factor $2 q$ out of $4 q^{2}$ .

$y (2 q (2 q) - 2 p q)$

Step 10.1.2

Factor $2 q$ out of $- 2 p q$ .

$y (2 q (2 q) + 2 q (- p))$

Step 10.1.3

Factor $2 q$ out of $2 q (2 q) + 2 q (- p)$ .

$y (2 q (2 q - p))$

Step 10.2

Remove unnecessary parentheses.

$y \cdot 2 q (2 q - p)$