Algebra Examples

$(a^{2}) (2 a^{3}) (a^{2} - 8 a + 9)$

Step 1

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 1.1

Move $a^{3}$ .

$a^{3} a^{2} \cdot 2 (a^{2} - 8 a + 9)$

Step 1.2

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

$a^{3 + 2} \cdot 2 (a^{2} - 8 a + 9)$

Step 1.3

Add $3$ and $2$ .

$a^{5} \cdot 2 (a^{2} - 8 a + 9)$

Step 2

Move $2$ to the left of $a^{5}$ .

$2 \cdot a^{5} (a^{2} - 8 a + 9)$

Step 3

Apply the distributive property.

$2 a^{5} a^{2} + 2 a^{5} (- 8 a) + 2 a^{5} \cdot 9$

Step 4

Simplify.

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Step 4.1

Multiply $a^{5}$ by $a^{2}$ by adding the exponents.

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Step 4.1.1

Move $a^{2}$ .

$2 (a^{2} a^{5}) + 2 a^{5} (- 8 a) + 2 a^{5} \cdot 9$

Step 4.1.2

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

$2 a^{2 + 5} + 2 a^{5} (- 8 a) + 2 a^{5} \cdot 9$

Step 4.1.3

Add $2$ and $5$ .

$2 a^{7} + 2 a^{5} (- 8 a) + 2 a^{5} \cdot 9$

Step 4.2

Rewrite using the commutative property of multiplication.

$2 a^{7} + 2 \cdot - 8 a^{5} a + 2 a^{5} \cdot 9$

Step 4.3

Multiply $9$ by $2$ .

$2 a^{7} + 2 \cdot - 8 a^{5} a + 18 a^{5}$

Step 5

Simplify each term.

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Step 5.1

Multiply $a^{5}$ by $a$ by adding the exponents.

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Step 5.1.1

Move $a$ .

$2 a^{7} + 2 \cdot - 8 (a \cdot a^{5}) + 18 a^{5}$

Step 5.1.2

Multiply $a$ by $a^{5}$ .

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Step 5.1.2.1

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

$2 a^{7} + 2 \cdot - 8 (a^{1} a^{5}) + 18 a^{5}$

Step 5.1.2.2

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

$2 a^{7} + 2 \cdot - 8 a^{1 + 5} + 18 a^{5}$

Step 5.1.3

Add $1$ and $5$ .

$2 a^{7} + 2 \cdot - 8 a^{6} + 18 a^{5}$

Step 5.2

Multiply $2$ by $- 8$ .

$2 a^{7} - 16 a^{6} + 18 a^{5}$