Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x^{2} + 2)}^{2}$ as $(x^{2} + 2) (x^{2} + 2)$ .

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

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

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Step 1.3.1.1.1

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

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

Step 1.3.1.1.2

Add $2$ and $2$ .

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

Step 1.3.1.2

Move $2$ to the left of $x^{2}$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

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

Step 1.3.2

Add $2 x^{2}$ and $2 x^{2}$ .

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

Step 2

Add $4$ and $2$ .

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