Solve left(3+xright)^2-2(x-4)-left(x-2right)^2

$${ \left(3+x \right) }^{ 2 } -2(x-4)- { \left(x-2 \right) }^{ 2 }$$

Evaluate

$$8x+13$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+x\right)^{2}.

$$9+6x+x^{2}-2\left(x-4\right)-\left(x-2\right)^{2}$$

Use the distributive property to multiply -2 by x-4.

$$9+6x+x^{2}-2x+8-\left(x-2\right)^{2}$$

Combine 6x and -2x to get 4x.

$$9+4x+x^{2}+8-\left(x-2\right)^{2}$$

Add 9 and 8 to get 17.

$$17+4x+x^{2}-\left(x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$17+4x+x^{2}-\left(x^{2}-4x+4\right)$$

To find the opposite of x^{2}-4x+4, find the opposite of each term.

$$17+4x+x^{2}-x^{2}+4x-4$$

Combine x^{2} and -x^{2} to get 0.

$$17+4x+4x-4$$

Combine 4x and 4x to get 8x.

$$17+8x-4$$

Subtract 4 from 17 to get 13.

$$13+8x$$

Expand

$$8x+13$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+x\right)^{2}.

$$9+6x+x^{2}-2\left(x-4\right)-\left(x-2\right)^{2}$$

Use the distributive property to multiply -2 by x-4.

$$9+6x+x^{2}-2x+8-\left(x-2\right)^{2}$$

Combine 6x and -2x to get 4x.

$$9+4x+x^{2}+8-\left(x-2\right)^{2}$$

Add 9 and 8 to get 17.

$$17+4x+x^{2}-\left(x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$17+4x+x^{2}-\left(x^{2}-4x+4\right)$$

To find the opposite of x^{2}-4x+4, find the opposite of each term.

$$17+4x+x^{2}-x^{2}+4x-4$$

Combine x^{2} and -x^{2} to get 0.

$$17+4x+4x-4$$

Combine 4x and 4x to get 8x.

$$17+8x-4$$

Subtract 4 from 17 to get 13.

$$13+8x$$