Algebra Examples

$y = {(x + 3)}^{2} + 53$

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 ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y = (x + 3) (x + 3) + 53$

Step 2.2

Expand $(x + 3) (x + 3)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$y = x (x + 3) + 3 (x + 3) + 53$

Step 2.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot 3 + 3 (x + 3) + 53$

Step 2.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3 + 53$

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 $x$ .

$y = x^{2} + x \cdot 3 + 3 x + 3 \cdot 3 + 53$

Step 2.3.1.2

Move $3$ to the left of $x$ .

$y = x^{2} + 3 \cdot x + 3 x + 3 \cdot 3 + 53$

Step 2.3.1.3

Multiply $3$ by $3$ .

$y = x^{2} + 3 x + 3 x + 9 + 53$

Step 2.3.2

Add $3 x$ and $3 x$ .

$y = x^{2} + 6 x + 9 + 53$

Step 3

Add $9$ and $53$ .

$y = x^{2} + 6 x + 62$

Step 4