Solve 3(x+2)^2-(x+4)^2

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply 3 by x^{2}+4x+4.

$$3x^{2}+12x+12-\left(x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$3x^{2}+12x+12-\left(x^{2}+8x+16\right)$$

To find the opposite of x^{2}+8x+16, find the opposite of each term.

$$3x^{2}+12x+12-x^{2}-8x-16$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}+12x+12-8x-16$$

Combine 12x and -8x to get 4x.

$$2x^{2}+4x+12-16$$

Subtract 16 from 12 to get -4.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply 3 by x^{2}+4x+4.

$$3x^{2}+12x+12-\left(x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$3x^{2}+12x+12-\left(x^{2}+8x+16\right)$$

To find the opposite of x^{2}+8x+16, find the opposite of each term.

$$3x^{2}+12x+12-x^{2}-8x-16$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}+12x+12-8x-16$$

Combine 12x and -8x to get 4x.

$$2x^{2}+4x+12-16$$

Subtract 16 from 12 to get -4.

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