Basic Math Examples

$(a + 2) (a^{2} - 8 a + 8)$

Step 1

Expand $(a + 2) (a^{2} - 8 a + 8)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

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 $1$ .

$a^{1} a^{2} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.1.1.2

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

$a^{1 + 2} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.1.2

Add $1$ and $2$ .

$a^{3} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$a^{3} - 8 a \cdot a + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.3

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

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Step 2.1.3.1

Move $a$ .

$a^{3} - 8 (a \cdot a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.3.2

Multiply $a$ by $a$ .

$a^{3} - 8 a^{2} + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.4

Move $8$ to the left of $a$ .

$a^{3} - 8 a^{2} + 8 \cdot a + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Step 2.1.5

Multiply $- 8$ by $2$ .

$a^{3} - 8 a^{2} + 8 a + 2 a^{2} - 16 a + 2 \cdot 8$

Step 2.1.6

Multiply $2$ by $8$ .

$a^{3} - 8 a^{2} + 8 a + 2 a^{2} - 16 a + 16$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 8 a^{2}$ and $2 a^{2}$ .

$a^{3} - 6 a^{2} + 8 a - 16 a + 16$

Step 2.2.2

Subtract $16 a$ from $8 a$ .

$a^{3} - 6 a^{2} - 8 a + 16$