Basic Math Examples

$(q^{2} + 4) (q^{2} - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1

Simplify each term.

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Step 1.1

Expand $(q^{2} + 4) (q^{2} - 4)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$(q^{2} (q^{2} - 4) + 4 (q^{2} - 4)) (q - 2) + 2 q (q^{3} + 8)$

Step 1.1.2

Apply the distributive property.

$(q^{2} q^{2} + q^{2} \cdot - 4 + 4 (q^{2} - 4)) (q - 2) + 2 q (q^{3} + 8)$

Step 1.1.3

Apply the distributive property.

$(q^{2} q^{2} + q^{2} \cdot - 4 + 4 q^{2} + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.2

Combine the opposite terms in $q^{2} q^{2} + q^{2} \cdot - 4 + 4 q^{2} + 4 \cdot - 4$ .

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Step 1.2.1

Reorder the factors in the terms $q^{2} \cdot - 4$ and $4 q^{2}$ .

$(q^{2} q^{2} - 4 q^{2} + 4 q^{2} + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.2.2

Add $- 4 q^{2}$ and $4 q^{2}$ .

$(q^{2} q^{2} + 0 + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.2.3

Add $q^{2} q^{2}$ and $0$ .

$(q^{2} q^{2} + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

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

$(q^{2 + 2} + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.3.1.2

Add $2$ and $2$ .

$(q^{4} + 4 \cdot - 4) (q - 2) + 2 q (q^{3} + 8)$

Step 1.3.2

Multiply $4$ by $- 4$ .

$(q^{4} - 16) (q - 2) + 2 q (q^{3} + 8)$

Step 1.4

Expand $(q^{4} - 16) (q - 2)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$q^{4} (q - 2) - 16 (q - 2) + 2 q (q^{3} + 8)$

Step 1.4.2

Apply the distributive property.

$q^{4} q + q^{4} \cdot - 2 - 16 (q - 2) + 2 q (q^{3} + 8)$

Step 1.4.3

Apply the distributive property.

$q^{4} q + q^{4} \cdot - 2 - 16 q - 16 \cdot - 2 + 2 q (q^{3} + 8)$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $q^{4}$ by $q$ by adding the exponents.

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Step 1.5.1.1

Multiply $q^{4}$ by $q$ .

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Step 1.5.1.1.1

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

$q^{4} q^{1} + q^{4} \cdot - 2 - 16 q - 16 \cdot - 2 + 2 q (q^{3} + 8)$

Step 1.5.1.1.2

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

$q^{4 + 1} + q^{4} \cdot - 2 - 16 q - 16 \cdot - 2 + 2 q (q^{3} + 8)$

Step 1.5.1.2

Add $4$ and $1$ .

$q^{5} + q^{4} \cdot - 2 - 16 q - 16 \cdot - 2 + 2 q (q^{3} + 8)$

Step 1.5.2

Move $- 2$ to the left of $q^{4}$ .

$q^{5} - 2 \cdot q^{4} - 16 q - 16 \cdot - 2 + 2 q (q^{3} + 8)$

Step 1.5.3

Multiply $- 16$ by $- 2$ .

$q^{5} - 2 q^{4} - 16 q + 32 + 2 q (q^{3} + 8)$

Step 1.6

Apply the distributive property.

$q^{5} - 2 q^{4} - 16 q + 32 + 2 q \cdot q^{3} + 2 q \cdot 8$

Step 1.7

Multiply $q$ by $q^{3}$ by adding the exponents.

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Step 1.7.1

Move $q^{3}$ .

$q^{5} - 2 q^{4} - 16 q + 32 + 2 (q^{3} q) + 2 q \cdot 8$

Step 1.7.2

Multiply $q^{3}$ by $q$ .

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Step 1.7.2.1

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

$q^{5} - 2 q^{4} - 16 q + 32 + 2 (q^{3} q^{1}) + 2 q \cdot 8$

Step 1.7.2.2

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

$q^{5} - 2 q^{4} - 16 q + 32 + 2 q^{3 + 1} + 2 q \cdot 8$

Step 1.7.3

Add $3$ and $1$ .

$q^{5} - 2 q^{4} - 16 q + 32 + 2 q^{4} + 2 q \cdot 8$

Step 1.8

Multiply $8$ by $2$ .

$q^{5} - 2 q^{4} - 16 q + 32 + 2 q^{4} + 16 q$

Step 2

Combine the opposite terms in $q^{5} - 2 q^{4} - 16 q + 32 + 2 q^{4} + 16 q$ .

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Step 2.1

Add $- 2 q^{4}$ and $2 q^{4}$ .

$q^{5} - 16 q + 32 + 0 + 16 q$

Step 2.2

Add $q^{5} - 16 q + 32$ and $0$ .

$q^{5} - 16 q + 32 + 16 q$

Step 2.3

Add $- 16 q$ and $16 q$ .

$q^{5} + 0 + 32$

Step 2.4

Add $q^{5}$ and $0$ .

$q^{5} + 32$