Precalculus Examples

$y = {(x + 5)}^{2} + 9$

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.

Tap for more steps...

Step 2.1

Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$y = (x + 5) (x + 5) + 9$

Step 2.2

Expand $(x + 5) (x + 5)$ using the FOIL Method.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

$y = x (x + 5) + 5 (x + 5) + 9$

Step 2.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot 5 + 5 (x + 5) + 9$

Step 2.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5 + 9$

Step 2.3

Simplify and combine like terms.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 5 + 5 x + 5 \cdot 5 + 9$

Step 2.3.1.2

Move $5$ to the left of $x$ .

$y = x^{2} + 5 \cdot x + 5 x + 5 \cdot 5 + 9$

Step 2.3.1.3

Multiply $5$ by $5$ .

$y = x^{2} + 5 x + 5 x + 25 + 9$

Step 2.3.2

Add $5 x$ and $5 x$ .

$y = x^{2} + 10 x + 25 + 9$

Step 3

Add $25$ and $9$ .

$y = x^{2} + 10 x + 34$

Step 4