Solve 4(-1+h)^2+2(-1+h)-4

$$4 ( - 1 + h ) ^ { 2 } + 2 ( - 1 + h ) - 4$$

Evaluate

$$4h^{2}-6h-2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-1+h\right)^{2}.

$$4\left(1-2h+h^{2}\right)+2\left(-1+h\right)-4$$

Use the distributive property to multiply 4 by 1-2h+h^{2}.

$$4-8h+4h^{2}+2\left(-1+h\right)-4$$

Use the distributive property to multiply 2 by -1+h.

$$4-8h+4h^{2}-2+2h-4$$

Subtract 2 from 4 to get 2.

$$2-8h+4h^{2}+2h-4$$

Combine -8h and 2h to get -6h.

$$2-6h+4h^{2}-4$$

Subtract 4 from 2 to get -2.

$$-2-6h+4h^{2}$$

Expand

$$4h^{2}-6h-2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-1+h\right)^{2}.

$$4\left(1-2h+h^{2}\right)+2\left(-1+h\right)-4$$

Use the distributive property to multiply 4 by 1-2h+h^{2}.

$$4-8h+4h^{2}+2\left(-1+h\right)-4$$

Use the distributive property to multiply 2 by -1+h.

$$4-8h+4h^{2}-2+2h-4$$

Subtract 2 from 4 to get 2.

$$2-8h+4h^{2}+2h-4$$

Combine -8h and 2h to get -6h.

$$2-6h+4h^{2}-4$$

Subtract 4 from 2 to get -2.

$$-2-6h+4h^{2}$$