Solve (x+u)^2-x(2u-x)

$$( x + u ) ^ { 2 } - x ( 2 u - x )$$

Evaluate

$$2x^{2}+u^{2}$$

Solution Steps

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

$$x^{2}+2xu+u^{2}-x\left(2u-x\right)$$

Use the distributive property to multiply x by 2u-x.

$$x^{2}+2xu+u^{2}-\left(2xu-x^{2}\right)$$

To find the opposite of 2xu-x^{2}, find the opposite of each term.

$$x^{2}+2xu+u^{2}-2xu+x^{2}$$

Combine 2xu and -2xu to get 0.

$$x^{2}+u^{2}+x^{2}$$

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

$$2x^{2}+u^{2}$$

Expand

$$2x^{2}+u^{2}$$

Solution Steps

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

$$x^{2}+2xu+u^{2}-x\left(2u-x\right)$$

Use the distributive property to multiply x by 2u-x.

$$x^{2}+2xu+u^{2}-\left(2xu-x^{2}\right)$$

To find the opposite of 2xu-x^{2}, find the opposite of each term.

$$x^{2}+2xu+u^{2}-2xu+x^{2}$$

Combine 2xu and -2xu to get 0.

$$x^{2}+u^{2}+x^{2}$$

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

$$2x^{2}+u^{2}$$