Algebra Examples

$x^{2} + 6 x - 27 = (x + 9) (x - 3)$

Step 1

Simplify $(x + 9) (x - 3)$ .

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Step 1.1

Rewrite.

$x^{2} + 6 x - 27 = 0 + 0 + (x + 9) (x - 3)$

Step 1.2

Simplify by adding zeros.

$x^{2} + 6 x - 27 = (x + 9) (x - 3)$

Step 1.3

Expand $(x + 9) (x - 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x^{2} + 6 x - 27 = x (x - 3) + 9 (x - 3)$

Step 1.3.2

Apply the distributive property.

$x^{2} + 6 x - 27 = x \cdot x + x \cdot - 3 + 9 (x - 3)$

Step 1.3.3

Apply the distributive property.

$x^{2} + 6 x - 27 = x \cdot x + x \cdot - 3 + 9 x + 9 \cdot - 3$

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 $x$ .

$x^{2} + 6 x - 27 = x^{2} + x \cdot - 3 + 9 x + 9 \cdot - 3$

Step 1.4.1.2

Move $- 3$ to the left of $x$ .

$x^{2} + 6 x - 27 = x^{2} - 3 \cdot x + 9 x + 9 \cdot - 3$

Step 1.4.1.3

Multiply $9$ by $- 3$ .

$x^{2} + 6 x - 27 = x^{2} - 3 x + 9 x - 27$

Step 1.4.2

Add $- 3 x$ and $9 x$ .

$x^{2} + 6 x - 27 = x^{2} + 6 x - 27$

Step 2

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

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Step 2.1

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

$x^{2} + 6 x - 27 - x^{2} = 6 x - 27$

Step 2.2

Subtract $6 x$ from both sides of the equation.

$x^{2} + 6 x - 27 - x^{2} - 6 x = - 27$

Step 2.3

Combine the opposite terms in $x^{2} + 6 x - 27 - x^{2} - 6 x$ .

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Step 2.3.1

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

$6 x - 27 + 0 - 6 x = - 27$

Step 2.3.2

Add $6 x - 27$ and $0$ .

$6 x - 27 - 6 x = - 27$

Step 2.3.3

Subtract $6 x$ from $6 x$ .

$0 - 27 = - 27$

Step 2.3.4

Subtract $27$ from $0$ .

$- 27 = - 27$

Step 3

Since $- 27 = - 27$ , the equation will always be true.

Always true