Algebra Examples

{(x^{2} + 7)}^{2}

${(x^{2} + 7)}^{2}$

Step 1

Rewrite

{(x^{2} + 7)}^{2}

${(x^{2} + 7)}^{2}$ as

(x^{2} + 7) (x^{2} + 7)

$(x^{2} + 7) (x^{2} + 7)$ .

(x^{2} + 7) (x^{2} + 7)

$(x^{2} + 7) (x^{2} + 7)$

Step 2

Expand

(x^{2} + 7) (x^{2} + 7)

$(x^{2} + 7) (x^{2} + 7)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

x^{2} (x^{2} + 7) + 7 (x^{2} + 7)

$x^{2} (x^{2} + 7) + 7 (x^{2} + 7)$

Step 2.2

Apply the distributive property.

x^{2} x^{2} + x^{2} \cdot 7 + 7 (x^{2} + 7)

$x^{2} x^{2} + x^{2} \cdot 7 + 7 (x^{2} + 7)$

Step 2.3

Apply the distributive property.

x^{2} x^{2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7

$x^{2} x^{2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

x^{2} x^{2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7

$x^{2} x^{2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

x^{2}

$x^{2}$ by

x^{2}

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

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Step 3.1.1.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

x^{2 + 2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7

$x^{2 + 2} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Step 3.1.1.2

Add

2

$2$ and

2

$2$ .

x^{4} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7

$x^{4} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

x^{4} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7

$x^{4} + x^{2} \cdot 7 + 7 x^{2} + 7 \cdot 7$

Step 3.1.2

Move

7

$7$ to the left of

x^{2}

$x^{2}$ .

x^{4} + 7 \cdot x^{2} + 7 x^{2} + 7 \cdot 7

$x^{4} + 7 \cdot x^{2} + 7 x^{2} + 7 \cdot 7$

Step 3.1.3

Multiply

7

$7$ by

7

$7$ .

x^{4} + 7 x^{2} + 7 x^{2} + 49

$x^{4} + 7 x^{2} + 7 x^{2} + 49$

x^{4} + 7 x^{2} + 7 x^{2} + 49

$x^{4} + 7 x^{2} + 7 x^{2} + 49$

Step 3.2

Add

7 x^{2}

$7 x^{2}$ and

7 x^{2}

$7 x^{2}$ .

x^{4} + 14 x^{2} + 49

$x^{4} + 14 x^{2} + 49$

x^{4} + 14 x^{2} + 49

$x^{4} + 14 x^{2} + 49$

{(x^{2} + 7)}^{2}

${(x^{2} + 7)}^{2}$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$