Question

What is The factors of 2x2 + xy - 3y² ?

Answer 1

Answer: (2x+3y) and (x-y)

Given:

$2x^2+xy-3y^2$

We can factor the given expression by grouping. We can rewrite the following expression:

$\begin{gathered} ax^2+bxy-cy^2 \\ \Rightarrow(ax^2+uxy)+(vxy-cy^2) \end{gathered}$

Given that:

a = 2

b = 1

c = -3

uv = ac

uv = 2(-3)

uv = -6

*Factor -6:

u = -2

v = 3

We now have:

$\begin{gathered} 2x^{2}+xy-3y^{2} \\ \Rightarrow(2x^2-2xy)+(3xy-3y^2) \end{gathered}$

We can now factor the expression easily:

$\begin{gathered} \begin{equation*} (2x^2-2xy)+(3xy-3y^2) \end{equation*} \\ \Rightarrow2x(x^-y)+3y(x-y^) \\ \Rightarrow(2x+3y)(x-y) \end{gathered}$

Therefore, its factors would be (2x+3y) and (x-y)