Write in Standard Form y=(2x+1)^2-9

$y = {(2 x + 1)}^{2} - 9$

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.

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

$y = (2 x + 1) (2 x + 1) - 9$

Expand $(2 x + 1) (2 x + 1)$ using the FOIL Method.

Apply the distributive property.

$y = 2 x (2 x + 1) + 1 (2 x + 1) - 9$

Apply the distributive property.

$y = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1) - 9$

Apply the distributive property.

$y = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1 - 9$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 2 \cdot (2 x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1 - 9$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$y = 2 \cdot (2 (x \cdot x)) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1 - 9$

Multiply $x$ by $x$ .

$y = 2 \cdot (2 x^{2}) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1 - 9$

Multiply $2$ by $2$ .

$y = 4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1 - 9$

Multiply $2$ by $1$ .

$y = 4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1 - 9$

Multiply $2 x$ by $1$ .

$y = 4 x^{2} + 2 x + 2 x + 1 \cdot 1 - 9$

Multiply $1$ by $1$ .

$y = 4 x^{2} + 2 x + 2 x + 1 - 9$

Add $2 x$ and $2 x$ .

$y = 4 x^{2} + 4 x + 1 - 9$

Step 3

Subtract $9$ from $1$ .

$y = 4 x^{2} + 4 x - 8$

Step 4