Algebra Examples

$y = {(x - 9)}^{2} + 2 x$

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(x - 9)}^{2}$ as $(x - 9) (x - 9)$ .

$y = (x - 9) (x - 9) + 2 x$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$y = x (x - 9) - 9 (x - 9) + 2 x$

Step 2.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 (x - 9) + 2 x$

Step 2.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 x - 9 \cdot - 9 + 2 x$

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 $x$ .

$y = x^{2} + x \cdot - 9 - 9 x - 9 \cdot - 9 + 2 x$

Step 2.3.1.2

Move $- 9$ to the left of $x$ .

$y = x^{2} - 9 \cdot x - 9 x - 9 \cdot - 9 + 2 x$

Step 2.3.1.3

Multiply $- 9$ by $- 9$ .

$y = x^{2} - 9 x - 9 x + 81 + 2 x$

Step 2.3.2

Subtract $9 x$ from $- 9 x$ .

$y = x^{2} - 18 x + 81 + 2 x$

Step 3

Add $- 18 x$ and $2 x$ .

$y = x^{2} - 16 x + 81$

Step 4