Algebra Examples

$8 x^{2} (4 x^{2} + 4 y^{6})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$8 x^{2} (4 x^{2}) + 8 x^{2} (4 y^{6})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$8 \cdot 4 x^{2} x^{2} + 8 x^{2} (4 y^{6})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$8 \cdot 4 x^{2} x^{2} + 8 \cdot 4 x^{2} y^{6}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x^{2}$ .

$8 \cdot 4 (x^{2} x^{2}) + 8 \cdot 4 x^{2} y^{6}$

Step 2.1.2

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

$8 \cdot 4 x^{2 + 2} + 8 \cdot 4 x^{2} y^{6}$

Step 2.1.3

Add $2$ and $2$ .

$8 \cdot 4 x^{4} + 8 \cdot 4 x^{2} y^{6}$

Step 2.2

Multiply $8$ by $4$ .

$32 x^{4} + 8 \cdot 4 x^{2} y^{6}$

Step 2.3

Multiply $8$ by $4$ .

$32 x^{4} + 32 x^{2} y^{6}$