Solve f(x+h)=-4(x+h)^2-7(x+h)+6

$$f ( x + h ) = - 4 ( x + h ) ^ { 2 } - 7 ( x + h ) + 6$$

Evaluate

$$-4\left(x+h\right)^{2}-7h-7x+6$$

Solution Steps

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

$$-4\left(x^{2}+2xh+h^{2}\right)-7\left(x+h\right)+6$$

Use the distributive property to multiply -4 by x^{2}+2xh+h^{2}.

$$-4x^{2}-8xh-4h^{2}-7\left(x+h\right)+6$$

Use the distributive property to multiply -7 by x+h.

$$-4x^{2}-8xh-4h^{2}-7x-7h+6$$

Expand

$$6-7h-4h^{2}-7x-8hx-4x^{2}$$

Solution Steps

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

$$-4\left(x^{2}+2xh+h^{2}\right)-7\left(x+h\right)+6$$

Use the distributive property to multiply -4 by x^{2}+2xh+h^{2}.

$$-4x^{2}-8xh-4h^{2}-7\left(x+h\right)+6$$

Use the distributive property to multiply -7 by x+h.

$$-4x^{2}-8xh-4h^{2}-7x-7h+6$$