Solve y-b-(y-b)^2

$$y - b - ( y - b ) ^ { 2 }$$

Evaluate

$$\left(b-y\right)\left(y-b-1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(y-b\right)^{2}.

$$y-b-\left(y^{2}-2yb+b^{2}\right)$$

To find the opposite of y^{2}-2yb+b^{2}, find the opposite of each term.

$$y-b-y^{2}+2yb-b^{2}$$

Expand

$$-y^{2}+2by+y-b^{2}-b$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(y-b\right)^{2}.

$$y-b-\left(y^{2}-2yb+b^{2}\right)$$

To find the opposite of y^{2}-2yb+b^{2}, find the opposite of each term.

$$y-b-y^{2}+2yb-b^{2}$$