Algebra Examples

${(x - 2)}^{2} - 4$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

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

$(x - 2) (x - 2) - 4$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$x (x - 2) - 2 (x - 2) - 4$

Step 2.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 (x - 2) - 4$

Step 2.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 - 4$

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 $x$ .

$x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 - 4$

Step 2.3.1.2

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

$x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 - 4$

Step 2.3.1.3

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x - 2 x + 4 - 4$

Step 2.3.2

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

$x^{2} - 4 x + 4 - 4$

Step 3

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

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Step 3.1

Subtract $4$ from $4$ .

$x^{2} - 4 x + 0$

Step 3.2

Add $x^{2} - 4 x$ and $0$ .

$x^{2} - 4 x$