Solve 1-2a-2b-3(a+b)^2

$$1 - 2 a - 2 b - 3 ( a + b ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply -3 by a^{2}+2ab+b^{2}.

$$1-2a-2b-3a^{2}-6ab-3b^{2}$$

Expand

$$1-2b-3b^{2}-2a-6ab-3a^{2}$$

Solution Steps

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

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

Use the distributive property to multiply -3 by a^{2}+2ab+b^{2}.

$$1-2a-2b-3a^{2}-6ab-3b^{2}$$