Solve -(2*5p-1*5q)^2-(1-5p-2-5q)^2

$$- ( 2 \cdot 5 p - 1 \cdot 5 q ) ^ { 2 } - ( 1 - 5 p - 2 - 5 q ) ^ { 2 }$$

Evaluate

$$-\left(5p+5q+1\right)^{2}-25\left(2p-q\right)^{2}$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\left(10p-1\times 5q\right)^{2}-\left(1-5p-2-5q\right)^{2}$$

Multiply 1 and 5 to get 5.

$$-\left(10p-5q\right)^{2}-\left(1-5p-2-5q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10p-5q\right)^{2}.

$$-\left(100p^{2}-100pq+25q^{2}\right)-\left(1-5p-2-5q\right)^{2}$$

To find the opposite of 100p^{2}-100pq+25q^{2}, find the opposite of each term.

$$-100p^{2}+100pq-25q^{2}-\left(1-5p-2-5q\right)^{2}$$

Subtract 2 from 1 to get -1.

$$-100p^{2}+100pq-25q^{2}-\left(-1-5p-5q\right)^{2}$$

Square -1-5p-5q.

$$-100p^{2}+100pq-25q^{2}-\left(25p^{2}+50pq+10p+25q^{2}+10q+1\right)$$

To find the opposite of 25p^{2}+50pq+10p+25q^{2}+10q+1, find the opposite of each term.

$$-100p^{2}+100pq-25q^{2}-25p^{2}-50pq-10p-25q^{2}-10q-1$$

Combine -100p^{2} and -25p^{2} to get -125p^{2}.

$$-125p^{2}+100pq-25q^{2}-50pq-10p-25q^{2}-10q-1$$

Combine 100pq and -50pq to get 50pq.

$$-125p^{2}+50pq-25q^{2}-10p-25q^{2}-10q-1$$

Combine -25q^{2} and -25q^{2} to get -50q^{2}.

$$-125p^{2}+50pq-50q^{2}-10p-10q-1$$

Expand

$$-125p^{2}+50pq-10p-50q^{2}-10q-1$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\left(10p-1\times 5q\right)^{2}-\left(1-5p-2-5q\right)^{2}$$

Multiply 1 and 5 to get 5.

$$-\left(10p-5q\right)^{2}-\left(1-5p-2-5q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10p-5q\right)^{2}.

$$-\left(100p^{2}-100pq+25q^{2}\right)-\left(1-5p-2-5q\right)^{2}$$

To find the opposite of 100p^{2}-100pq+25q^{2}, find the opposite of each term.

$$-100p^{2}+100pq-25q^{2}-\left(1-5p-2-5q\right)^{2}$$

Subtract 2 from 1 to get -1.

$$-100p^{2}+100pq-25q^{2}-\left(-1-5p-5q\right)^{2}$$

Square -1-5p-5q.

$$-100p^{2}+100pq-25q^{2}-\left(25p^{2}+50pq+10p+25q^{2}+10q+1\right)$$

To find the opposite of 25p^{2}+50pq+10p+25q^{2}+10q+1, find the opposite of each term.

$$-100p^{2}+100pq-25q^{2}-25p^{2}-50pq-10p-25q^{2}-10q-1$$

Combine -100p^{2} and -25p^{2} to get -125p^{2}.

$$-125p^{2}+100pq-25q^{2}-50pq-10p-25q^{2}-10q-1$$

Combine 100pq and -50pq to get 50pq.

$$-125p^{2}+50pq-25q^{2}-10p-25q^{2}-10q-1$$

Combine -25q^{2} and -25q^{2} to get -50q^{2}.

$$-125p^{2}+50pq-50q^{2}-10p-10q-1$$