Algebra Examples

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

Step 1

Multiply the exponents in ${({(x^{2} + 1)}^{2})}^{2}$ .

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Step 1.1

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

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

Step 1.2

Multiply $2$ by $2$ .

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

Step 2

Use the Binomial Theorem.

${(x^{2})}^{4} + 4 {(x^{2})}^{3} \cdot 1 + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 3.1.1

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

$x^{2 \cdot 4} + 4 {(x^{2})}^{3} \cdot 1 + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.1.2

Multiply $2$ by $4$ .

$x^{8} + 4 {(x^{2})}^{3} \cdot 1 + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.2

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

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Step 3.2.1

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

$x^{8} + 4 x^{2 \cdot 3} \cdot 1 + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.2.2

Multiply $2$ by $3$ .

$x^{8} + 4 x^{6} \cdot 1 + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.3

Multiply $4$ by $1$ .

$x^{8} + 4 x^{6} + 6 {(x^{2})}^{2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.4

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

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Step 3.4.1

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

$x^{8} + 4 x^{6} + 6 x^{2 \cdot 2} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.4.2

Multiply $2$ by $2$ .

$x^{8} + 4 x^{6} + 6 x^{4} \cdot 1^{2} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.5

One to any power is one.

$x^{8} + 4 x^{6} + 6 x^{4} \cdot 1 + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.6

Multiply $6$ by $1$ .

$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} \cdot 1^{3} + 1^{4}$

Step 3.7

One to any power is one.

$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} \cdot 1 + 1^{4}$

Step 3.8

Multiply $4$ by $1$ .

$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 1^{4}$

Step 3.9

One to any power is one.

$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 1$