Algebra Examples

$f (x) = 5 {(x - 1)}^{2} - 5$

Step 1

Rewrite the function as an equation.

$y = 5 {(x - 1)}^{2} - 5$

Step 2

Simplify $5 {(x - 1)}^{2} - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$y = 5 ((x - 1) (x - 1)) - 5$

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

$y = 5 (x (x - 1) - 1 (x - 1)) - 5$

Step 2.1.2.2

Apply the distributive property.

$y = 5 (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 5$

Step 2.1.2.3

Apply the distributive property.

$y = 5 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 5$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$y = 5 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) - 5$

Step 2.1.3.1.2

Move $- 1$ to the left of $x$ .

$y = 5 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 5$

Step 2.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$y = 5 (x^{2} - x - 1 x - 1 \cdot - 1) - 5$

Step 2.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$y = 5 (x^{2} - x - x - 1 \cdot - 1) - 5$

Step 2.1.3.1.5

Multiply $- 1$ by $- 1$ .

$y = 5 (x^{2} - x - x + 1) - 5$

Step 2.1.3.2

Subtract $x$ from $- x$ .

$y = 5 (x^{2} - 2 x + 1) - 5$

Step 2.1.4

Apply the distributive property.

$y = 5 x^{2} + 5 (- 2 x) + 5 \cdot 1 - 5$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $- 2$ by $5$ .

$y = 5 x^{2} - 10 x + 5 \cdot 1 - 5$

Step 2.1.5.2

Multiply $5$ by $1$ .

$y = 5 x^{2} - 10 x + 5 - 5$

Step 2.2

Combine the opposite terms in $5 x^{2} - 10 x + 5 - 5$ .

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Step 2.2.1

Subtract $5$ from $5$ .

$y = 5 x^{2} - 10 x + 0$

Step 2.2.2

Add $5 x^{2} - 10 x$ and $0$ .

$y = 5 x^{2} - 10 x$