Solve [1/2a-(c+2b)^2]

$$[ \frac { 1 } { 2 } a - ( c + 2 b ) ^ { 2 } ]$$

Evaluate

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

Solution Steps

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

$$\frac{1}{2}a-\left(c^{2}+4cb+4b^{2}\right)$$

To find the opposite of c^{2}+4cb+4b^{2}, find the opposite of each term.

$$\frac{1}{2}a-c^{2}-4cb-4b^{2}$$

Expand

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

Solution Steps

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

$$\frac{1}{2}a-\left(c^{2}+4cb+4b^{2}\right)$$

To find the opposite of c^{2}+4cb+4b^{2}, find the opposite of each term.

$$\frac{1}{2}a-c^{2}-4cb-4b^{2}$$