Basic Math Examples

$(3 q + 6) \cdot (7 q^{2})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$3 q (7 q^{2}) + 6 (7 q^{2})$

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 7 q \cdot q^{2} + 6 (7 q^{2})$

Step 1.2.2

Multiply $7$ by $6$ .

$3 \cdot 7 q \cdot q^{2} + 42 q^{2}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $q^{2}$ .

$3 \cdot 7 (q^{2} q) + 42 q^{2}$

Step 2.1.2

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

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Step 2.1.2.1

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

$3 \cdot 7 (q^{2} q^{1}) + 42 q^{2}$

Step 2.1.2.2

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

$3 \cdot 7 q^{2 + 1} + 42 q^{2}$

Step 2.1.3

Add $2$ and $1$ .

$3 \cdot 7 q^{3} + 42 q^{2}$

Step 2.2

Multiply $3$ by $7$ .

$21 q^{3} + 42 q^{2}$