Algebra Examples

$2 x^{2} (9 x^{2} - 16)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$2 x^{2} (9 x^{2}) + 2 x^{2} \cdot - 16$

Step 2.2

Simplify the expression.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 9 x^{2} x^{2} + 2 x^{2} \cdot - 16$

Step 2.2.2

Multiply $- 16$ by $2$ .

$2 \cdot 9 x^{2} x^{2} - 32 x^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{2}$ .

$2 \cdot 9 (x^{2} x^{2}) - 32 x^{2}$

Step 3.1.2

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

$2 \cdot 9 x^{2 + 2} - 32 x^{2}$

Step 3.1.3

Add $2$ and $2$ .

$2 \cdot 9 x^{4} - 32 x^{2}$

Step 3.2

Multiply $2$ by $9$ .

$18 x^{4} - 32 x^{2}$