Basic Math Examples

$3 a {(2 a - 3)}^{2} + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(2 a - 3)}^{2}$ as $(2 a - 3) (2 a - 3)$ .

$3 a ((2 a - 3) (2 a - 3)) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.2

Expand $(2 a - 3) (2 a - 3)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 a (2 a (2 a - 3) - 3 (2 a - 3)) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.2.2

Apply the distributive property.

$3 a (2 a (2 a) + 2 a \cdot - 3 - 3 (2 a - 3)) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.2.3

Apply the distributive property.

$3 a (2 a (2 a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$3 a (2 \cdot 2 a \cdot a + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.3.1.2.1

Move $a$ .

$3 a (2 \cdot 2 (a \cdot a) + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.2.2

Multiply $a$ by $a$ .

$3 a (2 \cdot 2 a^{2} + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.3

Multiply $2$ by $2$ .

$3 a (4 a^{2} + 2 a \cdot - 3 - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.4

Multiply $- 3$ by $2$ .

$3 a (4 a^{2} - 6 a - 3 (2 a) - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.5

Multiply $2$ by $- 3$ .

$3 a (4 a^{2} - 6 a - 6 a - 3 \cdot - 3) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.1.6

Multiply $- 3$ by $- 3$ .

$3 a (4 a^{2} - 6 a - 6 a + 9) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.3.2

Subtract $6 a$ from $- 6 a$ .

$3 a (4 a^{2} - 12 a + 9) + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.4

Apply the distributive property.

$3 a (4 a^{2}) + 3 a (- 12 a) + 3 a \cdot 9 + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.5

Simplify.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$3 \cdot 4 a \cdot a^{2} + 3 a (- 12 a) + 3 a \cdot 9 + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.5.2

Rewrite using the commutative property of multiplication.

$3 \cdot 4 a \cdot a^{2} + 3 \cdot - 12 a \cdot a + 3 a \cdot 9 + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.5.3

Multiply $9$ by $3$ .

$3 \cdot 4 a \cdot a^{2} + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 1.6.1.1

Move $a^{2}$ .

$3 \cdot 4 (a^{2} a) + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.1.2

Multiply $a^{2}$ by $a$ .

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Step 1.6.1.2.1

Raise $a$ to the power of $1$ .

$3 \cdot 4 (a^{2} a^{1}) + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \cdot 4 a^{2 + 1} + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.1.3

Add $2$ and $1$ .

$3 \cdot 4 a^{3} + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.2

Multiply $3$ by $4$ .

$12 a^{3} + 3 \cdot - 12 a \cdot a + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.3

Multiply $a$ by $a$ by adding the exponents.

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Step 1.6.3.1

Move $a$ .

$12 a^{3} + 3 \cdot - 12 (a \cdot a) + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.3.2

Multiply $a$ by $a$ .

$12 a^{3} + 3 \cdot - 12 a^{2} + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.6.4

Multiply $3$ by $- 12$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{2} (a - 5) - 2 a {(a + 2)}^{2}$

Step 1.7

Apply the distributive property.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{2} a + 4 a^{2} \cdot - 5 - 2 a {(a + 2)}^{2}$

Step 1.8

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 1.8.1

Move $a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 (a \cdot a^{2}) + 4 a^{2} \cdot - 5 - 2 a {(a + 2)}^{2}$

Step 1.8.2

Multiply $a$ by $a^{2}$ .

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Step 1.8.2.1

Raise $a$ to the power of $1$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 (a^{1} a^{2}) + 4 a^{2} \cdot - 5 - 2 a {(a + 2)}^{2}$

Step 1.8.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{1 + 2} + 4 a^{2} \cdot - 5 - 2 a {(a + 2)}^{2}$

Step 1.8.3

Add $1$ and $2$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} + 4 a^{2} \cdot - 5 - 2 a {(a + 2)}^{2}$

Step 1.9

Multiply $- 5$ by $4$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a {(a + 2)}^{2}$

Step 1.10

Rewrite ${(a + 2)}^{2}$ as $(a + 2) (a + 2)$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a ((a + 2) (a + 2))$

Step 1.11

Expand $(a + 2) (a + 2)$ using the FOIL Method.

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Step 1.11.1

Apply the distributive property.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a (a + 2) + 2 (a + 2))$

Step 1.11.2

Apply the distributive property.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a \cdot a + a \cdot 2 + 2 (a + 2))$

Step 1.11.3

Apply the distributive property.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a \cdot a + a \cdot 2 + 2 a + 2 \cdot 2)$

Step 1.12

Simplify and combine like terms.

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Step 1.12.1

Simplify each term.

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Step 1.12.1.1

Multiply $a$ by $a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a^{2} + a \cdot 2 + 2 a + 2 \cdot 2)$

Step 1.12.1.2

Move $2$ to the left of $a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a^{2} + 2 \cdot a + 2 a + 2 \cdot 2)$

Step 1.12.1.3

Multiply $2$ by $2$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a^{2} + 2 a + 2 a + 4)$

Step 1.12.2

Add $2 a$ and $2 a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a (a^{2} + 4 a + 4)$

Step 1.13

Apply the distributive property.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a \cdot a^{2} - 2 a (4 a) - 2 a \cdot 4$

Step 1.14

Simplify.

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Step 1.14.1

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 1.14.1.1

Move $a^{2}$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 (a^{2} a) - 2 a (4 a) - 2 a \cdot 4$

Step 1.14.1.2

Multiply $a^{2}$ by $a$ .

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Step 1.14.1.2.1

Raise $a$ to the power of $1$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 (a^{2} a^{1}) - 2 a (4 a) - 2 a \cdot 4$

Step 1.14.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{2 + 1} - 2 a (4 a) - 2 a \cdot 4$

Step 1.14.1.3

Add $2$ and $1$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 2 a (4 a) - 2 a \cdot 4$

Step 1.14.2

Rewrite using the commutative property of multiplication.

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 2 \cdot 4 a \cdot a - 2 a \cdot 4$

Step 1.14.3

Multiply $4$ by $- 2$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 2 \cdot 4 a \cdot a - 8 a$

Step 1.15

Simplify each term.

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Step 1.15.1

Multiply $a$ by $a$ by adding the exponents.

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Step 1.15.1.1

Move $a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 2 \cdot 4 (a \cdot a) - 8 a$

Step 1.15.1.2

Multiply $a$ by $a$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 2 \cdot 4 a^{2} - 8 a$

Step 1.15.2

Multiply $- 2$ by $4$ .

$12 a^{3} - 36 a^{2} + 27 a + 4 a^{3} - 20 a^{2} - 2 a^{3} - 8 a^{2} - 8 a$

Step 2

Simplify by adding terms.

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Step 2.1

Add $12 a^{3}$ and $4 a^{3}$ .

$16 a^{3} - 36 a^{2} + 27 a - 20 a^{2} - 2 a^{3} - 8 a^{2} - 8 a$

Step 2.2

Subtract $2 a^{3}$ from $16 a^{3}$ .

$14 a^{3} - 36 a^{2} + 27 a - 20 a^{2} - 8 a^{2} - 8 a$

Step 2.3

Subtract $20 a^{2}$ from $- 36 a^{2}$ .

$14 a^{3} - 56 a^{2} + 27 a - 8 a^{2} - 8 a$

Step 2.4

Subtract $8 a^{2}$ from $- 56 a^{2}$ .

$14 a^{3} - 64 a^{2} + 27 a - 8 a$

Step 2.5

Subtract $8 a$ from $27 a$ .

$14 a^{3} - 64 a^{2} + 19 a$