Solve (2.5p-1.5q)^2-(1.5p-2.5q)^2

$$( 2.5 p - 1.5 q ) ^ { 2 } - ( 1.5 p - 2.5 q ) ^ { 2 }$$

Evaluate

$$4\left(p^{2}-q^{2}\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2.5p-1.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(1.5p-2.5q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1.5p-2.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(2.25p^{2}-7.5pq+6.25q^{2}\right)$$

To find the opposite of 2.25p^{2}-7.5pq+6.25q^{2}, find the opposite of each term.

$$6.25p^{2}-7.5pq+2.25q^{2}-2.25p^{2}+7.5pq-6.25q^{2}$$

Combine 6.25p^{2} and -2.25p^{2} to get 4p^{2}.

$$4p^{2}-7.5pq+2.25q^{2}+7.5pq-6.25q^{2}$$

Combine -7.5pq and 7.5pq to get 0.

$$4p^{2}+2.25q^{2}-6.25q^{2}$$

Combine 2.25q^{2} and -6.25q^{2} to get -4q^{2}.

$$4p^{2}-4q^{2}$$

Expand

$$4p^{2}-4q^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2.5p-1.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(1.5p-2.5q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1.5p-2.5q\right)^{2}.

$$6.25p^{2}-7.5pq+2.25q^{2}-\left(2.25p^{2}-7.5pq+6.25q^{2}\right)$$

To find the opposite of 2.25p^{2}-7.5pq+6.25q^{2}, find the opposite of each term.

$$6.25p^{2}-7.5pq+2.25q^{2}-2.25p^{2}+7.5pq-6.25q^{2}$$

Combine 6.25p^{2} and -2.25p^{2} to get 4p^{2}.

$$4p^{2}-7.5pq+2.25q^{2}+7.5pq-6.25q^{2}$$

Combine -7.5pq and 7.5pq to get 0.

$$4p^{2}+2.25q^{2}-6.25q^{2}$$

Combine 2.25q^{2} and -6.25q^{2} to get -4q^{2}.

$$4p^{2}-4q^{2}$$