Solve a-[2/3(b-1)^2]=

$$a - [ \frac { 2 } { 3 } ( b - 1 ) ^ { 2 } ] =$$

Evaluate

$$-\frac{2\left(b-1\right)^{2}}{3}+a$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-1\right)^{2}.

$$a-\frac{2}{3}\left(b^{2}-2b+1\right)$$

Use the distributive property to multiply -\frac{2}{3} by b^{2}-2b+1.

$$a-\frac{2}{3}b^{2}+\frac{4}{3}b-\frac{2}{3}$$

Expand

$$-\frac{2b^{2}}{3}+\frac{4b}{3}+a-\frac{2}{3}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-1\right)^{2}.

$$a-\frac{2}{3}\left(b^{2}-2b+1\right)$$

Use the distributive property to multiply -\frac{2}{3} by b^{2}-2b+1.

$$a-\frac{2}{3}b^{2}+\frac{4}{3}b-\frac{2}{3}$$