Question

Given the trinomial, what is the value of the coefficient B in the factored form? 2x2 + 4xy − 48y2 = 2(x + By)(x − 4y) −12 12 −6 6

Answer 1

Answer:

B is 6.

Step-by-step explanation:

We are trying to find a value for $B$ such that:

$2x^2+4xy-48y^2=2(x+By)(x-4y)$ is true for every $x,y$.

So let's choose $x=0,y=1$:

$2(0)^2+4(0)(1)-48(1)^2=2(0+B(1))(0-4(1))$

$2(0)+0-48=2(B)(-4)$

$0-48=-8B$

$-48=-8B$

Divide both sides by -8:

$\frac{-48}{-8}=B$

$6=B$

$B=6$

Note: I didn't want to choose y to be 0 because the value of B would disappear from the equation. So you should be able to have chosen any x and y except for y=0 to solve the equation for B.

Check:

So let's check and use foil to multiply out the right hand side.

$(x+6y)(x-4y)$

$x(x)+x(-4y)+6y(x)+6y(-4y)$

$x^2-4xy+6xy-24y^2$

$x^2+2xy-24y^2$

There was a 2 in front of that multplicapltiation:

$2(x+6y)(x-4y)$

$2(x^2+2xy-24y^2)$

$2x^2+4xy-48y^2$

This is exactly what we have on the left hand side of your given equation.