Algebra Examples

$(x + 10) (x - 4) = {(x + 2)}^{2}$

Step 1

Simplify $(x + 10) (x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + (x + 10) (x - 4) = {(x + 2)}^{2}$

Step 1.2

Simplify by adding zeros.

$(x + 10) (x - 4) = {(x + 2)}^{2}$

Step 1.3

Expand $(x + 10) (x - 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x (x - 4) + 10 (x - 4) = {(x + 2)}^{2}$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 10 (x - 4) = {(x + 2)}^{2}$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 10 x + 10 \cdot - 4 = {(x + 2)}^{2}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + 10 x + 10 \cdot - 4 = {(x + 2)}^{2}$

Step 1.4.1.2

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + 10 x + 10 \cdot - 4 = {(x + 2)}^{2}$

Step 1.4.1.3

Multiply $10$ by $- 4$ .

$x^{2} - 4 x + 10 x - 40 = {(x + 2)}^{2}$

Step 1.4.2

Add $- 4 x$ and $10 x$ .

$x^{2} + 6 x - 40 = {(x + 2)}^{2}$

Step 2

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

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Step 2.1

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

$x^{2} + 6 x - 40 = (x + 2) (x + 2)$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$x^{2} + 6 x - 40 = x (x + 2) + 2 (x + 2)$

Step 2.2.2

Apply the distributive property.

$x^{2} + 6 x - 40 = x \cdot x + x \cdot 2 + 2 (x + 2)$

Step 2.2.3

Apply the distributive property.

$x^{2} + 6 x - 40 = x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + 6 x - 40 = x^{2} + x \cdot 2 + 2 x + 2 \cdot 2$

Step 2.3.1.2

Move $2$ to the left of $x$ .

$x^{2} + 6 x - 40 = x^{2} + 2 \cdot x + 2 x + 2 \cdot 2$

Step 2.3.1.3

Multiply $2$ by $2$ .

$x^{2} + 6 x - 40 = x^{2} + 2 x + 2 x + 4$

Step 2.3.2

Add $2 x$ and $2 x$ .

$x^{2} + 6 x - 40 = x^{2} + 4 x + 4$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 6 x - 40 - x^{2} = 4 x + 4$

Step 3.2

Subtract $4 x$ from both sides of the equation.

$x^{2} + 6 x - 40 - x^{2} - 4 x = 4$

Step 3.3

Combine the opposite terms in $x^{2} + 6 x - 40 - x^{2} - 4 x$ .

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Step 3.3.1

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

$6 x - 40 + 0 - 4 x = 4$

Step 3.3.2

Add $6 x - 40$ and $0$ .

$6 x - 40 - 4 x = 4$

Step 3.4

Subtract $4 x$ from $6 x$ .

$2 x - 40 = 4$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $40$ to both sides of the equation.

$2 x = 4 + 40$

Step 4.2

Add $4$ and $40$ .

$2 x = 44$

Step 5

Divide each term in $2 x = 44$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 44$ by $2$ .

$\frac{2 x}{2} = \frac{44}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{44}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{44}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $44$ by $2$ .

$x = 22$