Solve 4(x+h)^2-6(x+h)

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

Evaluate

$$2\left(x+h\right)\left(2x+2h-3\right)$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -6 by x+h.

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

Expand

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -6 by x+h.

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