Question

factorize given in figure

Answer 1

Question.

(ax+by)²+(bx-ay)²

Answer

Use Identity (a+b)²=a²+b²+2ab

And (a-b)²=a²+b²-2ab

Above Term can be written as

(ax+by)²+(bx-ay)²

[(ax)²+(by)²+2axby]+[(bx)²+(ay)²-2bxay]

=(ax²)+(by)²$\cancel{+2axby}$+(bx)²+(ay)²$\cancel{-2bxay}$

=(ax)²+(by)²+(bx)²+(ay)²

=[a²x²+b²x²]+[b²y²+a²y²]

=x²(a²+b²)+y²(b²+a²)

=(a²+b²)(x²+y²)

$\boxed{\boxed{\mathbf{Answer=( { a}^{2} + {b}^{2} ) ( {x}^{2} + {y}^{2}) }}}$