Solve left(x-3right)^2-left(x-4right)-1+1

$${ \left(x-3 \right) }^{ 2 } - \left( x-4 \right) -1+1$$

Evaluate

$$x^{2}-7x+13$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9-\left(x-4\right)-1+1$$

To find the opposite of x-4, find the opposite of each term.

$$x^{2}-6x+9-x+4-1+1$$

Combine -6x and -x to get -7x.

$$x^{2}-7x+9+4-1+1$$

Add 9 and 4 to get 13.

$$x^{2}-7x+13-1+1$$

Subtract 1 from 13 to get 12.

$$x^{2}-7x+12+1$$

Add 12 and 1 to get 13.

$$x^{2}-7x+13$$

Expand

$$x^{2}-7x+13$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9-\left(x-4\right)-1+1$$

To find the opposite of x-4, find the opposite of each term.

$$x^{2}-6x+9-x+4-1+1$$

Combine -6x and -x to get -7x.

$$x^{2}-7x+9+4-1+1$$

Add 9 and 4 to get 13.

$$x^{2}-7x+13-1+1$$

Subtract 1 from 13 to get 12.

$$x^{2}-7x+12+1$$

Add 12 and 1 to get 13.

$$x^{2}-7x+13$$