Question

$\text{Factorise the given expression:}ab(x^2+y^2)+xy(a^2+b^2)$

• A. $(bx+ay)(ax+by)$
• B. $(ax+by)$
• C. $(b{x}^2+a{y}^2)(ax+by)$
• D. $(b+a)(ax+by)$

Answer 1

The correct option is A $(bx+ay)(ax+by)$

$\text{Given expression:}ab(x^2+y^2)+xy(a^2+b^2)$

$\text{By applying the distributivity}\text{property we get,}$
$=ab{x}^2+ab{y}^2+a^{2}xy+b^{2}xy$

$\text{By regrouping the terms we get,}$
$=(ab{x}^2+a^{2}xy)+(ab{y}^2+b^{2}xy)$

$\text{By taking the common factors out,}\text{we get,}$
$=ax(bx+ay)+by(ay+bx)=(bx+ay)(ax+by)$

$\text{Thus,}ab(x^2+y^2)+xy(a^2+b^2)=(bx+ay)(ax+by).$