Solve (25p-15q)^2-(15p-25q)^2

$$( 25 p - 15 q ) ^ { 2 } - ( 15 p - 25 q ) ^ { 2 }$$

Evaluate

$$400\left(p^{2}-q^{2}\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(25p-15q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(15p-25q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15p-25q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(225p^{2}-750pq+625q^{2}\right)$$

To find the opposite of 225p^{2}-750pq+625q^{2}, find the opposite of each term.

$$625p^{2}-750pq+225q^{2}-225p^{2}+750pq-625q^{2}$$

Combine 625p^{2} and -225p^{2} to get 400p^{2}.

$$400p^{2}-750pq+225q^{2}+750pq-625q^{2}$$

Combine -750pq and 750pq to get 0.

$$400p^{2}+225q^{2}-625q^{2}$$

Combine 225q^{2} and -625q^{2} to get -400q^{2}.

$$400p^{2}-400q^{2}$$

Expand

$$400p^{2}-400q^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(25p-15q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(15p-25q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15p-25q\right)^{2}.

$$625p^{2}-750pq+225q^{2}-\left(225p^{2}-750pq+625q^{2}\right)$$

To find the opposite of 225p^{2}-750pq+625q^{2}, find the opposite of each term.

$$625p^{2}-750pq+225q^{2}-225p^{2}+750pq-625q^{2}$$

Combine 625p^{2} and -225p^{2} to get 400p^{2}.

$$400p^{2}-750pq+225q^{2}+750pq-625q^{2}$$

Combine -750pq and 750pq to get 0.

$$400p^{2}+225q^{2}-625q^{2}$$

Combine 225q^{2} and -625q^{2} to get -400q^{2}.

$$400p^{2}-400q^{2}$$