Algebra Examples

${(x - 8)}^{2} + (x - 8) - 15$

Step 1

Remove parentheses.

${(x - 8)}^{2} + x - 8 - 15$

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(x - 8)}^{2}$ as $(x - 8) (x - 8)$ .

$(x - 8) (x - 8) + x - 8 - 15$

Step 2.2

Expand $(x - 8) (x - 8)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$x (x - 8) - 8 (x - 8) + x - 8 - 15$

Step 2.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 8 (x - 8) + x - 8 - 15$

Step 2.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 8 x - 8 \cdot - 8 + x - 8 - 15$

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 $x$ .

$x^{2} + x \cdot - 8 - 8 x - 8 \cdot - 8 + x - 8 - 15$

Step 2.3.1.2

Move $- 8$ to the left of $x$ .

$x^{2} - 8 \cdot x - 8 x - 8 \cdot - 8 + x - 8 - 15$

Step 2.3.1.3

Multiply $- 8$ by $- 8$ .

$x^{2} - 8 x - 8 x + 64 + x - 8 - 15$

Step 2.3.2

Subtract $8 x$ from $- 8 x$ .

$x^{2} - 16 x + 64 + x - 8 - 15$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 16 x$ and $x$ .

$x^{2} - 15 x + 64 - 8 - 15$

Step 3.2

Simplify by subtracting numbers.

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Step 3.2.1

Subtract $8$ from $64$ .

$x^{2} - 15 x + 56 - 15$

Step 3.2.2

Subtract $15$ from $56$ .

$x^{2} - 15 x + 41$