Solve (x+5)(x-1)+left(x-2right)^2

$$(x+5)(x-1)+ { \left(x-2 \right) }^{ 2 }$$

Evaluate

$$2x^{2}-1$$

Solution Steps

Use the distributive property to multiply x+5 by x-1 and combine like terms.

$$x^{2}+4x-5+\left(x-2\right)^{2}$$

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

$$x^{2}+4x-5+x^{2}-4x+4$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+4x-5-4x+4$$

Combine 4x and -4x to get 0.

$$2x^{2}-5+4$$

Add -5 and 4 to get -1.

$$2x^{2}-1$$

Expand

$$2x^{2}-1$$

Solution Steps

Use the distributive property to multiply x+5 by x-1 and combine like terms.

$$x^{2}+4x-5+\left(x-2\right)^{2}$$

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

$$x^{2}+4x-5+x^{2}-4x+4$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+4x-5-4x+4$$

Combine 4x and -4x to get 0.

$$2x^{2}-5+4$$

Add -5 and 4 to get -1.

$$2x^{2}-1$$