Question

The factors of 2x^2 + xy - 3y^2 are

A (2x - 3y)(x + y)

B (2x + 3y)(x - y)

C (2x - y)(x + 3y)

D (2x + y)(x - 3y)​

Answer 1

Answer:

B. (2x + 3y)(x - y)

Step-by-step explanation:

$2x^{2} +xy-3y^{2}$               Write x y as a difference

$2x^{2} +3xy-2xy-3y^{2}$    Factor out x from the equation

$xx(2x+3y)-yx(2x+3y)$   Factor out 2x+3y from the expression

$(2x+3y)x(x-y)$               <----- Answer

Answer 2

The factors of  $2x^2 + xy - 3y^2$ are $(x - y) (2x+ 3y)$.

What are factors ?

Factors is a number or algebraic expression that divides another number or expression. i.e., with no remainder

We have,

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

Now,

Using the middle term split method,

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

Splitting the mid term;

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

Now taking commons,

$2x(x - y) + 3y(x - y)$

Now again taking common factors

We get,

$(x - y) (2x+ 3y)$

So, the factors of given expression are $(x - y) (2x+ 3y)$.

Hence, we can say that the factors of  $2x^2 + xy - 3y^2$ are $(x - y) (2x+ 3y)$ which are given in option $(B)$ .

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