Question 1. Factorize pqr + qr 2 − pr 2 − r 3

Question 1. Factorize 
pqr+q  r^{2}-pr^{2}-r^{3}

Factorization methods —


To factorize this expression we see that qr is common between first two terms and - r^{2} is common between the last two terms. So this expression can be dealt by taking commons out from respective pair of terms;

pqr+q  r^{2}-pr^{2}-r^{3}

=qr(p+r)-r ^{2}(p+r)

If we put brackets again for the sake of understanding we see it as;

=[qr(p+r)-r ^{2}(p+r)]

Now we can see that (p+r) is common here – taking it out, we get;

=(p+r)[qr-r ^{2}]

So, these are two factors of the expression uptill now;

Butif seen closely in the second factor viz [qr-r ^{2}], r is again a common to be found — take it out – we get;

=r(p+r)[q-r ]

So, finally r , (p+r) and (q-r) are three factors of the given expression.