Solve left(x-1right)^2+7(x-1)+10

$${ \left(x-1 \right) }^{ 2 } +7(x-1)+10$$

Evaluate

$$\left(x+1\right)\left(x+4\right)$$

Solution Steps

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

$$x^{2}-2x+1+7\left(x-1\right)+10$$

Use the distributive property to multiply 7 by x-1.

$$x^{2}-2x+1+7x-7+10$$

Combine -2x and 7x to get 5x.

$$x^{2}+5x+1-7+10$$

Subtract 7 from 1 to get -6.

$$x^{2}+5x-6+10$$

Add -6 and 10 to get 4.

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

Expand

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

Solution Steps

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

$$x^{2}-2x+1+7\left(x-1\right)+10$$

Use the distributive property to multiply 7 by x-1.

$$x^{2}-2x+1+7x-7+10$$

Combine -2x and 7x to get 5x.

$$x^{2}+5x+1-7+10$$

Subtract 7 from 1 to get -6.

$$x^{2}+5x-6+10$$

Add -6 and 10 to get 4.

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