Question

factorize p(p-r)-q(q-r)
I know the answer but not the working method.

Answer 1

Distribute p and q to brackets..

Answer 2

p(p-r)-q(q-r)
= p^2 -pr - q^2 + qr
= p^2 - q^2 - pr + qr
= (p+q)(p-q) - r (p-q)
= ...?

Answer 3

\[\large p^2 - pr - q^2 + qr\]

Answer 4

Identity used: \(a^2-b^2 = (a+b)(a-b)\)

Answer 5

the answer is \[(p-q)(p+q-r)\]

Answer 6

I haven't done the whole question! I left one step for you :)

Answer 7

exactly.... thats the answer i got.... n it is absolutely correct... tnx

Answer 8

\[p^2 - pr - q^2 + qr \implies (p^2 -q^2) + qr - pr \implies (p+q)(p-q) + r(q-p)\]

\[\large (p+q)(p-q) + r(q-p) \implies (p-q)[p+q - r]\]

Answer 9

You're welcome!

Answer 10

:)