Solve 42ab-(3a+7b)^2

$$42 a b - ( 3 a + 7 b ) ^ { 2 }$$

Evaluate

$$-9a^{2}-49b^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+7b\right)^{2}.

$$42ab-\left(9a^{2}+42ab+49b^{2}\right)$$

To find the opposite of 9a^{2}+42ab+49b^{2}, find the opposite of each term.

$$42ab-9a^{2}-42ab-49b^{2}$$

Combine 42ab and -42ab to get 0.

$$-9a^{2}-49b^{2}$$

Expand

$$-9a^{2}-49b^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+7b\right)^{2}.

$$42ab-\left(9a^{2}+42ab+49b^{2}\right)$$

To find the opposite of 9a^{2}+42ab+49b^{2}, find the opposite of each term.

$$42ab-9a^{2}-42ab-49b^{2}$$

Combine 42ab and -42ab to get 0.

$$-9a^{2}-49b^{2}$$