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

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

Evaluate

$$x^{2}+3x-2$$

Solution Steps

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

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

Use the distributive property to multiply 5 by x-1.

$$x^{2}-2x+1+5x-5+2$$

Combine -2x and 5x to get 3x.

$$x^{2}+3x+1-5+2$$

Subtract 5 from 1 to get -4.

$$x^{2}+3x-4+2$$

Add -4 and 2 to get -2.

$$x^{2}+3x-2$$

Expand

$$x^{2}+3x-2$$

Solution Steps

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

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

Use the distributive property to multiply 5 by x-1.

$$x^{2}-2x+1+5x-5+2$$

Combine -2x and 5x to get 3x.

$$x^{2}+3x+1-5+2$$

Subtract 5 from 1 to get -4.

$$x^{2}+3x-4+2$$

Add -4 and 2 to get -2.

$$x^{2}+3x-2$$