Algebra Examples

${(1 + x^{2})}^{3}$

Step 1

Use the Binomial Theorem.

$1^{3} + 3 \cdot 1^{2} x^{2} + 3 \cdot 1 {(x^{2})}^{2} + {(x^{2})}^{3}$

Step 2

Simplify each term.

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Step 2.1

One to any power is one.

$1 + 3 \cdot 1^{2} x^{2} + 3 \cdot 1 {(x^{2})}^{2} + {(x^{2})}^{3}$

Step 2.2

One to any power is one.

$1 + 3 \cdot 1 x^{2} + 3 \cdot 1 {(x^{2})}^{2} + {(x^{2})}^{3}$

Step 2.3

Multiply $3$ by $1$ .

$1 + 3 x^{2} + 3 \cdot 1 {(x^{2})}^{2} + {(x^{2})}^{3}$

Step 2.4

Multiply $3$ by $1$ .

$1 + 3 x^{2} + 3 {(x^{2})}^{2} + {(x^{2})}^{3}$

Step 2.5

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 2.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$1 + 3 x^{2} + 3 x^{2 \cdot 2} + {(x^{2})}^{3}$

Step 2.5.2

Multiply $2$ by $2$ .

$1 + 3 x^{2} + 3 x^{4} + {(x^{2})}^{3}$

Step 2.6

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 2.6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$1 + 3 x^{2} + 3 x^{4} + x^{2 \cdot 3}$

Step 2.6.2

Multiply $2$ by $3$ .

$1 + 3 x^{2} + 3 x^{4} + x^{6}$