Algebra Examples

$(a - 6) (a^{2} + 6 a + 36)$

Step 1

Expand $(a - 6) (a^{2} + 6 a + 36)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (6 a) + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$a^{1} a^{2} + a (6 a) + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.1.1.2

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

$a^{1 + 2} + a (6 a) + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.1.2

Add $1$ and $2$ .

$a^{3} + a (6 a) + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$a^{3} + 6 a \cdot a + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.3

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

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Step 2.1.3.1

Move $a$ .

$a^{3} + 6 (a \cdot a) + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.3.2

Multiply $a$ by $a$ .

$a^{3} + 6 a^{2} + a \cdot 36 - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.4

Move $36$ to the left of $a$ .

$a^{3} + 6 a^{2} + 36 \cdot a - 6 a^{2} - 6 (6 a) - 6 \cdot 36$

Step 2.1.5

Multiply $6$ by $- 6$ .

$a^{3} + 6 a^{2} + 36 a - 6 a^{2} - 36 a - 6 \cdot 36$

Step 2.1.6

Multiply $- 6$ by $36$ .

$a^{3} + 6 a^{2} + 36 a - 6 a^{2} - 36 a - 216$

Step 2.2

Combine the opposite terms in $a^{3} + 6 a^{2} + 36 a - 6 a^{2} - 36 a - 216$ .

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Step 2.2.1

Subtract $6 a^{2}$ from $6 a^{2}$ .

$a^{3} + 36 a + 0 - 36 a - 216$

Step 2.2.2

Add $a^{3} + 36 a$ and $0$ .

$a^{3} + 36 a - 36 a - 216$

Step 2.2.3

Subtract $36 a$ from $36 a$ .

$a^{3} + 0 - 216$

Step 2.2.4

Add $a^{3}$ and $0$ .

$a^{3} - 216$