Precalculus Examples

{(x + 1)}^{2}

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

Step 1

Rewrite

{(x + 1)}^{2}

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

(x + 1) (x + 1)

$(x + 1) (x + 1)$ .

(x + 1) (x + 1)

$(x + 1) (x + 1)$

Step 2

Expand

(x + 1) (x + 1)

$(x + 1) (x + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

x (x + 1) + 1 (x + 1)

$x (x + 1) + 1 (x + 1)$

Step 2.2

Apply the distributive property.

x \cdot x + x \cdot 1 + 1 (x + 1)

$x \cdot x + x \cdot 1 + 1 (x + 1)$

Step 2.3

Apply the distributive property.

x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1

$x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1$

x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1

$x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1$

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

$x$ by

x

$x$ .

x^{2} + x \cdot 1 + 1 x + 1 \cdot 1

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

Step 3.1.2

Multiply

x

$x$ by

1

$1$ .

x^{2} + x + 1 x + 1 \cdot 1

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

Step 3.1.3

Multiply

x

$x$ by

1

$1$ .

x^{2} + x + x + 1 \cdot 1

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

Step 3.1.4

Multiply

1

$1$ by

1

$1$ .

x^{2} + x + x + 1

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

x^{2} + x + x + 1

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

Step 3.2

Add

x

$x$ and

x

$x$ .

x^{2} + 2 x + 1

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

x^{2} + 2 x + 1

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

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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