Solve (x+h)^2-6(x+h)^2-(x^2-6x)

$$( x + h ) ^ { 2 } - 6 ( x + h ) ^ { 2 } - ( x ^ { 2 } - 6 x )$$

Evaluate

$$-x\left(x-6\right)-5\left(x+h\right)^{2}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -6 by x^{2}+2xh+h^{2}.

$$x^{2}+2xh+h^{2}-6x^{2}-12xh-6h^{2}-\left(x^{2}-6x\right)$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}+2xh+h^{2}-12xh-6h^{2}-\left(x^{2}-6x\right)$$

Combine 2xh and -12xh to get -10xh.

$$-5x^{2}-10xh+h^{2}-6h^{2}-\left(x^{2}-6x\right)$$

Combine h^{2} and -6h^{2} to get -5h^{2}.

$$-5x^{2}-10xh-5h^{2}-\left(x^{2}-6x\right)$$

To find the opposite of x^{2}-6x, find the opposite of each term.

$$-5x^{2}-10xh-5h^{2}-x^{2}+6x$$

Combine -5x^{2} and -x^{2} to get -6x^{2}.

$$-6x^{2}-10xh-5h^{2}+6x$$

Expand

$$-6x^{2}-10hx+6x-5h^{2}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -6 by x^{2}+2xh+h^{2}.

$$x^{2}+2xh+h^{2}-6x^{2}-12xh-6h^{2}-\left(x^{2}-6x\right)$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}+2xh+h^{2}-12xh-6h^{2}-\left(x^{2}-6x\right)$$

Combine 2xh and -12xh to get -10xh.

$$-5x^{2}-10xh+h^{2}-6h^{2}-\left(x^{2}-6x\right)$$

Combine h^{2} and -6h^{2} to get -5h^{2}.

$$-5x^{2}-10xh-5h^{2}-\left(x^{2}-6x\right)$$

To find the opposite of x^{2}-6x, find the opposite of each term.

$$-5x^{2}-10xh-5h^{2}-x^{2}+6x$$

Combine -5x^{2} and -x^{2} to get -6x^{2}.

$$-6x^{2}-10xh-5h^{2}+6x$$