Question

Factorise the expression and then divide

(i) 5pq(p 2 − q 2) ÷ 2p(p + q)

Answer 1

$\large\sf{\underline{\underline{ \ Given \ : \ }}}$




$\sf\red{\implies {\dfrac{5pq \ ( p^2 \ - \ q^2 )}{2p \ ( p \ + \ q )}}}$




$\large\sf{\underline{\underline{ \ Solution \ : \ }}}$




$\sf{\implies {\dfrac{5pq \ [ \ ( p + q ) \ ( p - q ) \ ]}{2p \ ( p + q )}}}$





$\sf{\implies{\dfrac{5 {\cancel{p}} q \ [ \ {\cancel{(p + q)}} \ ( p - q ) \ ]}{2 {\cancel{p}} \ {\cancel{( p + q)}}}}}$




$\sf{\implies{\dfrac{5q ( p - q )}{2}}}$




$\sf{\implies {\dfrac{5}{2}} × q( p - q )}$




$\sf{\implies 2.5 \ q(p - q)}$




$\sf\blue{\implies 2.5 \ qp - 2.5 \ q^2}$




${\large{\boxed{\sf{Algebraic \ \ Identity \ :}}}}$



$\large\sf\purple{\implies \ a^2 - b^2 \ = \ ( a + b ) \ ( a - b)}$