Basic Math Examples

$q (5 q - 1) (5 q + 1)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$(q (5 q) + q \cdot - 1) (5 q + 1)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$(5 q \cdot q + q \cdot - 1) (5 q + 1)$

Step 1.2.2

Move $- 1$ to the left of $q$ .

$(5 q \cdot q - 1 \cdot q) (5 q + 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $q$ by $q$ by adding the exponents.

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Step 1.3.1.1

Move $q$ .

$(5 (q \cdot q) - 1 \cdot q) (5 q + 1)$

Step 1.3.1.2

Multiply $q$ by $q$ .

$(5 q^{2} - 1 \cdot q) (5 q + 1)$

Step 1.3.2

Rewrite $- 1 q$ as $- q$ .

$(5 q^{2} - q) (5 q + 1)$

Step 2

Expand $(5 q^{2} - q) (5 q + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 q^{2} (5 q + 1) - q (5 q + 1)$

Step 2.2

Apply the distributive property.

$5 q^{2} (5 q) + 5 q^{2} \cdot 1 - q (5 q + 1)$

Step 2.3

Apply the distributive property.

$5 q^{2} (5 q) + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 q^{2} q + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.2

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

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Step 3.1.2.1

Move $q$ .

$5 \cdot 5 (q \cdot q^{2}) + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.2.2

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

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Step 3.1.2.2.1

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

$5 \cdot 5 (q^{1} q^{2}) + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.2.2.2

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

$5 \cdot 5 q^{1 + 2} + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.2.3

Add $1$ and $2$ .

$5 \cdot 5 q^{3} + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.3

Multiply $5$ by $5$ .

$25 q^{3} + 5 q^{2} \cdot 1 - q (5 q) - q \cdot 1$

Step 3.1.4

Multiply $5$ by $1$ .

$25 q^{3} + 5 q^{2} - q (5 q) - q \cdot 1$

Step 3.1.5

Rewrite using the commutative property of multiplication.

$25 q^{3} + 5 q^{2} - 1 \cdot 5 q \cdot q - q \cdot 1$

Step 3.1.6

Multiply $q$ by $q$ by adding the exponents.

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Step 3.1.6.1

Move $q$ .

$25 q^{3} + 5 q^{2} - 1 \cdot 5 (q \cdot q) - q \cdot 1$

Step 3.1.6.2

Multiply $q$ by $q$ .

$25 q^{3} + 5 q^{2} - 1 \cdot 5 q^{2} - q \cdot 1$

Step 3.1.7

Multiply $- 1$ by $5$ .

$25 q^{3} + 5 q^{2} - 5 q^{2} - q \cdot 1$

Step 3.1.8

Multiply $- 1$ by $1$ .

$25 q^{3} + 5 q^{2} - 5 q^{2} - q$

Step 3.2

Subtract $5 q^{2}$ from $5 q^{2}$ .

$25 q^{3} + 0 - q$

Step 3.3

Add $25 q^{3}$ and $0$ .

$25 q^{3} - q$