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

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

Evaluate

$$-8b\left(a-b\right)$$

Solution Steps

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

$$a^{2}-6ab+9b^{2}-\left(a+b\right)^{2}$$

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

$$a^{2}-6ab+9b^{2}-\left(a^{2}+2ab+b^{2}\right)$$

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

$$a^{2}-6ab+9b^{2}-a^{2}-2ab-b^{2}$$

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

$$-6ab+9b^{2}-2ab-b^{2}$$

Combine -6ab and -2ab to get -8ab.

$$-8ab+9b^{2}-b^{2}$$

Combine 9b^{2} and -b^{2} to get 8b^{2}.

$$-8ab+8b^{2}$$

Expand

$$8b^{2}-8ab$$

Solution Steps

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

$$a^{2}-6ab+9b^{2}-\left(a+b\right)^{2}$$

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

$$a^{2}-6ab+9b^{2}-\left(a^{2}+2ab+b^{2}\right)$$

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

$$a^{2}-6ab+9b^{2}-a^{2}-2ab-b^{2}$$

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

$$-6ab+9b^{2}-2ab-b^{2}$$

Combine -6ab and -2ab to get -8ab.

$$-8ab+9b^{2}-b^{2}$$

Combine 9b^{2} and -b^{2} to get 8b^{2}.

$$-8ab+8b^{2}$$