Write in Standard Form 2(x+3)^2-(x+2)^2=16

$2 {(x + 3)}^{2} - {(x + 2)}^{2} = 16$

Step 1

Subtract $16$ from both sides of the equation.

$2 {(x + 3)}^{2} - {(x + 2)}^{2} - 16 = 0$

Step 2

Simplify $2 {(x + 3)}^{2} - {(x + 2)}^{2} - 16$ .

Simplify each term.

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

$2 ((x + 3) (x + 3)) - {(x + 2)}^{2} - 16 = 0$

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

Apply the distributive property.

$2 (x (x + 3) + 3 (x + 3)) - {(x + 2)}^{2} - 16 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot 3 + 3 (x + 3)) - {(x + 2)}^{2} - 16 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - {(x + 2)}^{2} - 16 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) - {(x + 2)}^{2} - 16 = 0$

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

$2 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) - {(x + 2)}^{2} - 16 = 0$

Multiply $3$ by $3$ .

$2 (x^{2} + 3 x + 3 x + 9) - {(x + 2)}^{2} - 16 = 0$

Add $3 x$ and $3 x$ .

$2 (x^{2} + 6 x + 9) - {(x + 2)}^{2} - 16 = 0$

Apply the distributive property.

$2 x^{2} + 2 (6 x) + 2 \cdot 9 - {(x + 2)}^{2} - 16 = 0$

Simplify.

Multiply $6$ by $2$ .

$2 x^{2} + 12 x + 2 \cdot 9 - {(x + 2)}^{2} - 16 = 0$

Multiply $2$ by $9$ .

$2 x^{2} + 12 x + 18 - {(x + 2)}^{2} - 16 = 0$

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

$2 x^{2} + 12 x + 18 - ((x + 2) (x + 2)) - 16 = 0$

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

Apply the distributive property.

$2 x^{2} + 12 x + 18 - (x (x + 2) + 2 (x + 2)) - 16 = 0$

Apply the distributive property.

$2 x^{2} + 12 x + 18 - (x \cdot x + x \cdot 2 + 2 (x + 2)) - 16 = 0$

Apply the distributive property.

$2 x^{2} + 12 x + 18 - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - 16 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 x^{2} + 12 x + 18 - (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) - 16 = 0$

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

$2 x^{2} + 12 x + 18 - (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) - 16 = 0$

Multiply $2$ by $2$ .

$2 x^{2} + 12 x + 18 - (x^{2} + 2 x + 2 x + 4) - 16 = 0$

Add $2 x$ and $2 x$ .

$2 x^{2} + 12 x + 18 - (x^{2} + 4 x + 4) - 16 = 0$

Apply the distributive property.

$2 x^{2} + 12 x + 18 - x^{2} - (4 x) - 1 \cdot 4 - 16 = 0$

Simplify.

Multiply $4$ by $- 1$ .

$2 x^{2} + 12 x + 18 - x^{2} - 4 x - 1 \cdot 4 - 16 = 0$

Multiply $- 1$ by $4$ .

$2 x^{2} + 12 x + 18 - x^{2} - 4 x - 4 - 16 = 0$

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} + 12 x + 18 - 4 x - 4 - 16 = 0$

Subtract $4 x$ from $12 x$ .

$x^{2} + 8 x + 18 - 4 - 16 = 0$

Subtract $4$ from $18$ .

$x^{2} + 8 x + 14 - 16 = 0$

Subtract $16$ from $14$ .

$x^{2} + 8 x - 2 = 0$

Step 3

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

$a x^{2} + b x + c = 0$

Step 4

The standard form is $x^{2} + 8 x - 2$ .

$x^{2} + 8 x - 2 = 0$

Step 5

Write in Standard Form 2(x+3)^2-(x+2)^2=16

Related Questions

Support LCMGCF.com by disabling your adblocker.