Divide : `8p^(3)-36p^(2)q+54pq^(2)-27q^(3)` by `4p^(2)-12pq+9q^(2)`

(p-q)^(2)+4pq

Add : 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq

Add : 3p^(2)q^(2) - 4pq + 5, - 10p^(2) q^(2), 15 + 9pq + 7p^(2)q^(2)

If p = -2, q = - 1 and r = 3, find the value of (i) p^(2) + q^(2) - r^(2) (ii) 2p^(2) - q^(2) + 3r^(2) (iii) p - q - r (iv) p^(3) + q^(3) + r^(3) + 3 pqr (v) 3p^(2) q + 5pq^(2) + 2 pqr (vi) p^(4) + q^(4) - r^(4)

{(p^(2)+3px+3pq+9qx)(p-3q)}-:(p^(2)-9q^(2))

Verify that (p-q) ( p ^(2) + pq + q ^(2)) = p ^(3) - q ^(3)

Subtract: 4pq - 5a^(2) - 3p^(2) "from" 5p^(2) + 3q^(2) - pq

If Delta=|[0,q,r],[q,r,p],[r,p,q]|, then |[rq-p^(2),pr-q^(2),pq-r^(2)],[rp-q^(2),pq-r^(2),rq-p^(2)],[pq-r^(2),rq-p^(2),pr-q^(2)]| is equal to

(a) Subtract 4a-7ab+3b+12 from 12a-9ab+5b(r) Subtract 3xy+5yz-7zx from 5xy-2yx+10xyz( ij ) Subtract 4p^(2)q-3pq+5pq^(2)-8p+7q-10 from 18-3p-11q+5pq-2pq^(2)+5p^(2)q

If two positive integers a and b are expressible in the form a=pq^(2) and b=p^(3)q;p,q being prime numbers,then LCM(a,b) is pq( b) p^(3)q^(3) (c) p^(3)q^(2)( d )p^(2)q^(2)