Solve -(6a-3b)^2-(3b+2a)^2=

$$- ( 6 a - 3 b ) ^ { 2 } - ( 3 b + 2 a ) ^ { 2 } =$$

Evaluate

$$-40a^{2}+24ab-18b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(6a-3b\right)^{2}.

$$-\left(36a^{2}-36ab+9b^{2}\right)-\left(3b+2a\right)^{2}$$

To find the opposite of 36a^{2}-36ab+9b^{2}, find the opposite of each term.

$$-36a^{2}+36ab-9b^{2}-\left(3b+2a\right)^{2}$$

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

$$-36a^{2}+36ab-9b^{2}-\left(9b^{2}+12ba+4a^{2}\right)$$

To find the opposite of 9b^{2}+12ba+4a^{2}, find the opposite of each term.

$$-36a^{2}+36ab-9b^{2}-9b^{2}-12ba-4a^{2}$$

Combine -9b^{2} and -9b^{2} to get -18b^{2}.

$$-36a^{2}+36ab-18b^{2}-12ba-4a^{2}$$

Combine 36ab and -12ba to get 24ab.

$$-36a^{2}+24ab-18b^{2}-4a^{2}$$

Combine -36a^{2} and -4a^{2} to get -40a^{2}.

$$-40a^{2}+24ab-18b^{2}$$

Expand

$$-40a^{2}+24ab-18b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(6a-3b\right)^{2}.

$$-\left(36a^{2}-36ab+9b^{2}\right)-\left(3b+2a\right)^{2}$$

To find the opposite of 36a^{2}-36ab+9b^{2}, find the opposite of each term.

$$-36a^{2}+36ab-9b^{2}-\left(3b+2a\right)^{2}$$

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

$$-36a^{2}+36ab-9b^{2}-\left(9b^{2}+12ba+4a^{2}\right)$$

To find the opposite of 9b^{2}+12ba+4a^{2}, find the opposite of each term.

$$-36a^{2}+36ab-9b^{2}-9b^{2}-12ba-4a^{2}$$

Combine -9b^{2} and -9b^{2} to get -18b^{2}.

$$-36a^{2}+36ab-18b^{2}-12ba-4a^{2}$$

Combine 36ab and -12ba to get 24ab.

$$-36a^{2}+24ab-18b^{2}-4a^{2}$$

Combine -36a^{2} and -4a^{2} to get -40a^{2}.

$$-40a^{2}+24ab-18b^{2}$$