Question

(p-q+r) ^2+(p-q-r) ^2

Answer 1

Step-by-step explanation:

(p-q+r)² + (p-q-r)²

{(p-q)+r}² + {(p-q)-r}²

(p-q)² + r² + 2r(p-q) + (p-q)² + r² - 2r(p-q)

2(p-q)² + 2r²

2{p²+q²-2pq} + 2r²

2{p² + q² + r² - 2pq)

Answer 2

Answer:

$\large\boxed{2p^2-4pq+2q^2+2r^2}$

Step-by-step explanation:

To solve this problem, first you have to use the distributive property.

Given:

(p-q+r)²+(p-q-r)²

Solutions:

First, used distributive property formula.

$\Large\boxed{\textnormal{DISTRIBUTIVE PROPERTY}}$

$\displaystyle A(B+C)=AB+AC$

$\displaystyle (p-q-r)^2=(p-q-r)(p-q+r)$

Add exponent.

$\displaystyle  (p-q-r)=(p-q-r)(p-q+r)^2$

$(p-q-r)^2=(p-q-r)(p-q+r)$

Solve.

$\displaystyle (p+r-q)(p+r-q)+(p-q-r)(p-q-r)$

Next, thing you do is expand.

$\displaystyle (p-q+r)(p-q+r)=-2pq+2pr+p^2+q^2-2qr+r^2$

Rewrite the whole problem down.

$\displaystyle -2pq+2pr+p^2+q^2-2qr+r^2+(p-q-r)(p-q-r)$

Solve.

$\displaystyle (p-q-r)(p-q-r)=-2pq-2pr+p^2+q^2+2qr+r^2$

Rewrite the whole problem again.

$\displaystyle -2pq+2pr+p^2+q^2-2qr+r^2-2pq-2pr+p^2+q^2+2qr+r^2$

Then, you solve.

$\displaystyle -2pq+2pr+p^2+q^2-2qr+r^2-2pq-2pr+p^2+q^2+2qr+r^2=\boxed{2p^2-4pq+2q^2+2r^2}$

$\large\boxed{2p^2-4pq+2q^2+2r^2}$

Therefore, the correct answer is 2p²-4pq+2q²+2r².