Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Expand $(x + h) (x + h)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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

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 $x$ by $x$ .

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

Step 1.3.1.2

Multiply $h$ by $h$ .

$x^{2} + x h + h x + h^{2} - x^{2}$

$x^{2} + x h + h x + h^{2} - x^{2}$

Step 1.3.2

Add $x h$ and $h x$ .

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Step 1.3.2.1

Reorder $x$ and $h$ .

$x^{2} + h x + h x + h^{2} - x^{2}$

Step 1.3.2.2

Add $h x$ and $h x$ .

$x^{2} + 2 h x + h^{2} - x^{2}$

$x^{2} + 2 h x + h^{2} - x^{2}$

$x^{2} + 2 h x + h^{2} - x^{2}$

$x^{2} + 2 h x + h^{2} - x^{2}$

Step 2

Combine the opposite terms in $x^{2} + 2 h x + h^{2} - x^{2}$ .

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Step 2.1

Subtract $x^{2}$ from $x^{2}$ .

$2 h x + h^{2} + 0$

Step 2.2

Add $2 h x + h^{2}$ and $0$ .

$2 h x + h^{2}$

$2 h x + h^{2}$

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