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

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

Evaluate

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

Solution Steps

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

$$4a^{2}-12ab+9b^{2}-\left(3a-2b\right)^{2}$$

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

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

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

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

Combine 4a^{2} and -9a^{2} to get -5a^{2}.

$$-5a^{2}-12ab+9b^{2}+12ab-4b^{2}$$

Combine -12ab and 12ab to get 0.

$$-5a^{2}+9b^{2}-4b^{2}$$

Combine 9b^{2} and -4b^{2} to get 5b^{2}.

$$-5a^{2}+5b^{2}$$

Expand

$$5b^{2}-5a^{2}$$

Solution Steps

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

$$4a^{2}-12ab+9b^{2}-\left(3a-2b\right)^{2}$$

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

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

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

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

Combine 4a^{2} and -9a^{2} to get -5a^{2}.

$$-5a^{2}-12ab+9b^{2}+12ab-4b^{2}$$

Combine -12ab and 12ab to get 0.

$$-5a^{2}+9b^{2}-4b^{2}$$

Combine 9b^{2} and -4b^{2} to get 5b^{2}.

$$-5a^{2}+5b^{2}$$