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

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

Evaluate

$$9$$

Solution Steps

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

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

Use the distributive property to multiply -4 by x-1.

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

Use the distributive property to multiply -4x+4 by x+2 and combine like terms.

$$4x^{2}+4x+1-4x^{2}-4x+8$$

Combine 4x^{2} and -4x^{2} to get 0.

$$4x+1-4x+8$$

Combine 4x and -4x to get 0.

$$1+8$$

Add 1 and 8 to get 9.

$$9$$

Factor

$$3^{2}$$