Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

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Step 2.1.1

Move $a^{4}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $4$ and $2$ .

$4 a^{6} b^{3} (9 b^{2}) + 4 a^{2} b^{3} (- 4 a^{2}) + 4 a^{2} b^{3} \cdot 3$

Step 2.2

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

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Step 2.2.1

Move $a^{2}$ .

$4 a^{6} b^{3} (9 b^{2}) + 4 (a^{2} a^{2}) b^{3} \cdot - 4 + 4 a^{2} b^{3} \cdot 3$

Step 2.2.2

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

$4 a^{6} b^{3} (9 b^{2}) + 4 a^{2 + 2} b^{3} \cdot - 4 + 4 a^{2} b^{3} \cdot 3$

Step 2.2.3

Add $2$ and $2$ .

$4 a^{6} b^{3} (9 b^{2}) + 4 a^{4} b^{3} \cdot - 4 + 4 a^{2} b^{3} \cdot 3$

Step 2.3

Multiply $3$ by $4$ .

$4 a^{6} b^{3} (9 b^{2}) + 4 a^{4} b^{3} \cdot - 4 + 12 a^{2} b^{3}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $b^{2}$ .

$4 a^{6} (b^{2} b^{3}) \cdot 9 + 4 a^{4} b^{3} \cdot - 4 + 12 a^{2} b^{3}$

Step 3.1.2

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

$4 a^{6} b^{2 + 3} \cdot 9 + 4 a^{4} b^{3} \cdot - 4 + 12 a^{2} b^{3}$

Step 3.1.3

Add $2$ and $3$ .

$4 a^{6} b^{5} \cdot 9 + 4 a^{4} b^{3} \cdot - 4 + 12 a^{2} b^{3}$

Step 3.2

Multiply $9$ by $4$ .

$36 a^{6} b^{5} + 4 a^{4} b^{3} \cdot - 4 + 12 a^{2} b^{3}$

Step 3.3

Multiply $- 4$ by $4$ .

$36 a^{6} b^{5} - 16 a^{4} b^{3} + 12 a^{2} b^{3}$