Solve 3(x+h)^2+2(x+h)-7

$$3 ( x + h ) ^ { 2 } + 2 ( x + h ) - 7$$

Evaluate

$$3\left(x+h\right)^{2}+2h+2x-7$$

Solution Steps

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

$$3\left(x^{2}+2xh+h^{2}\right)+2\left(x+h\right)-7$$

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

$$3x^{2}+6xh+3h^{2}+2\left(x+h\right)-7$$

Use the distributive property to multiply 2 by x+h.

$$3x^{2}+6xh+3h^{2}+2x+2h-7$$

Expand

$$3x^{2}+6hx+2x+3h^{2}+2h-7$$

Solution Steps

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

$$3\left(x^{2}+2xh+h^{2}\right)+2\left(x+h\right)-7$$

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

$$3x^{2}+6xh+3h^{2}+2\left(x+h\right)-7$$

Use the distributive property to multiply 2 by x+h.

$$3x^{2}+6xh+3h^{2}+2x+2h-7$$