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

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

Evaluate

$$24ab$$

Solution Steps

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

$$1\left(9a^{2}+12ab+4b^{2}\right)-\left(3a-2b\right)^{2}$$

Use the distributive property to multiply 1 by 9a^{2}+12ab+4b^{2}.

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

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

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

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

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

Combine 9a^{2} and -9a^{2} to get 0.

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

Combine 12ab and 12ab to get 24ab.

$$24ab+4b^{2}-4b^{2}$$

Combine 4b^{2} and -4b^{2} to get 0.

$$24ab$$

Expand

$$24ab$$

Solution Steps

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

$$1\left(9a^{2}+12ab+4b^{2}\right)-\left(3a-2b\right)^{2}$$

Use the distributive property to multiply 1 by 9a^{2}+12ab+4b^{2}.

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

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

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

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

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

Combine 9a^{2} and -9a^{2} to get 0.

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

Combine 12ab and 12ab to get 24ab.

$$24ab+4b^{2}-4b^{2}$$

Combine 4b^{2} and -4b^{2} to get 0.

$$24ab$$