Precalculus Examples

${(x + 1)}^{2} = x^{3}$

Step 1

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

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Step 1.1

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

$(x + 1) (x + 1) = x^{3}$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$x (x + 1) + 1 (x + 1) = x^{3}$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 1 + 1 (x + 1) = x^{3}$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 = x^{3}$

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 $x$ .

$x^{2} + x \cdot 1 + 1 x + 1 \cdot 1 = x^{3}$

Step 1.3.1.2

Multiply $x$ by $1$ .

$x^{2} + x + 1 x + 1 \cdot 1 = x^{3}$

Step 1.3.1.3

Multiply $x$ by $1$ .

$x^{2} + x + x + 1 \cdot 1 = x^{3}$

Step 1.3.1.4

Multiply $1$ by $1$ .

$x^{2} + x + x + 1 = x^{3}$

Step 1.3.2

Add $x$ and $x$ .

$x^{2} + 2 x + 1 = x^{3}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.14789903$

Step 3