Question

Factorise
${x}^{2} + 5xy - 2y ^{2}$
​

Answer 1

Answer:

SOLUTION:-

\begin{gathered}{2x}^{2} - 5xy - {2y}^{2} \\ \\ = > {2x}^{2} - 5xy + {2y}^{2} = 0 \\ \\ = > {2x}^{2} - 4xy - xy + {2x}^{2} = 0 \\ \\ = > 2x(x -2y) - y(x - 2y) = 0 \\ \\ = > (x - 2y)(2x - y) = 0 \\ \\ = > x - 2y = 0 \: \: \: or \: \: \: 2x - y = 0 \\ \\ = > x = 2y \: \: or \: \: 2x = y \\ \\ = > x = 2y \: \: \: or \: \: x = \frac{y}{2}\end{gathered}

2x

2

−5xy−2y

2

=>2x

2

−5xy+2y

2

=0

=>2x

2

−4xy−xy+2x

2

=0

=>2x(x−2y)−y(x−2y)=0

=>(x−2y)(2x−y)=0

=>x−2y=0or2x−y=0

=>x=2yor2x=y

=>x=2yorx=

2

y

Hope it helps ☺️