Pre-Algebra Examples

$y = {(x - 2)}^{2} - 5$

Step 1

Simplify ${(x - 2)}^{2} - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$y = (x - 2) (x - 2) - 5$

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

$y = x (x - 2) - 2 (x - 2) - 5$

Step 1.1.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 (x - 2) - 5$

Step 1.1.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 - 5$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 - 5$

Step 1.1.3.1.2

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

$y = x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 - 5$

Step 1.1.3.1.3

Multiply $- 2$ by $- 2$ .

$y = x^{2} - 2 x - 2 x + 4 - 5$

Step 1.1.3.2

Subtract $2 x$ from $- 2 x$ .

$y = x^{2} - 4 x + 4 - 5$

Step 1.2

Subtract $5$ from $4$ .

$y = x^{2} - 4 x - 1$

Step 2

When solving for $y$ , $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x^{2}$