Solve 0.5(x+h)^2-(x+h)+3

$$0.5 ( x + h ) ^ { 2 } - ( x + h ) + 3$$

Evaluate

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

Solution Steps

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

$$0.5\left(x^{2}+2xh+h^{2}\right)-\left(x+h\right)+3$$

Use the distributive property to multiply 0.5 by x^{2}+2xh+h^{2}.

$$0.5x^{2}+xh+0.5h^{2}-\left(x+h\right)+3$$

To find the opposite of x+h, find the opposite of each term.

$$0.5x^{2}+xh+0.5h^{2}-x-h+3$$

Expand

$$hx+\frac{h^{2}}{2}+\frac{x^{2}}{2}-h-x+3$$

Solution Steps

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

$$0.5\left(x^{2}+2xh+h^{2}\right)-\left(x+h\right)+3$$

Use the distributive property to multiply 0.5 by x^{2}+2xh+h^{2}.

$$0.5x^{2}+xh+0.5h^{2}-\left(x+h\right)+3$$

To find the opposite of x+h, find the opposite of each term.

$$0.5x^{2}+xh+0.5h^{2}-x-h+3$$