Question

x^2+2xy-15y^2 factorize​

Answer 1

x² + 2xy - 15y²

= x² + 5xy - 3xy - 15y²
= x(x + 5y) - 3y(x + 5y)
= (x + 5y) (x - 3y)

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Answer 2

To factorize :  $x^{2} + 2xy - 15y^{2}$

Solution:

• To factorize $x^{2} + 2xy - 15y^{2}$ we apply the identity $(x-y)^{2}=x^{2}-2 x y+y^{2}$
• We add and subtract $y^{2}$ to balance the equation.

            $\begin{array}{l}=x^{2}-2 x y-15 y^{2}+y^{2}-y^{2} \\=x^{2}-2 x y+y^{2}-15 y^{2}-y^{2} \\=(x-y)^{2}-16 y^{2} \\=(x-y)^{2}-(4 y)^{2}\end{array}$

• Last step is the  difference between two squares  $a^{2}-b^{2}=(a-b)(a+b)$

          $a=(x-y)$  and $b = 4y$

         Then , we have  $(x-y)^{2}-(4 y)^{2}$

                           $=(x-y-4 y)(x-y+4 y)$

                           $=(x-5 y)(x+3 y)$

      Hence , factors of $x^{2} + 2xy - 15y^{2}$ are $( x- 5y ) ( x + 3y )$.