Solve (-5)(a+b)^2+20*3

$$( - 5 ) ( a + b ) ^ { 2 } + 20 \times 3$$

Evaluate

$$-5\left(a+b\right)^{2}+60$$

Solution Steps

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

$$-5\left(a^{2}+2ab+b^{2}\right)+20\times 3$$

Use the distributive property to multiply -5 by a^{2}+2ab+b^{2}.

$$-5a^{2}-10ab-5b^{2}+20\times 3$$

Multiply 20 and 3 to get 60.

$$-5a^{2}-10ab-5b^{2}+60$$

Expand

$$60-5b^{2}-10ab-5a^{2}$$

Solution Steps

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

$$-5\left(a^{2}+2ab+b^{2}\right)+20\times 3$$

Use the distributive property to multiply -5 by a^{2}+2ab+b^{2}.

$$-5a^{2}-10ab-5b^{2}+20\times 3$$

Multiply 20 and 3 to get 60.

$$-5a^{2}-10ab-5b^{2}+60$$