Answer:
B is 6.
Step-by-step explanation:
We are trying to find a value for [tex]B[/tex] such that:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)[/tex] is true for every [tex]x,y[/tex].
So let's choose [tex]x=0,y=1[/tex]:
[tex]2(0)^2+4(0)(1)-48(1)^2=2(0+B(1))(0-4(1))[/tex]
[tex]2(0)+0-48=2(B)(-4)[/tex]
[tex]0-48=-8B[/tex]
[tex]-48=-8B[/tex]
Divide both sides by -8:
[tex]\frac{-48}{-8}=B[/tex]
[tex]6=B[/tex]
[tex]B=6[/tex]
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.
[tex](x+6y)(x-4y)[/tex]
[tex]x(x)+x(-4y)+6y(x)+6y(-4y)[/tex]
[tex]x^2-4xy+6xy-24y^2[/tex]
[tex]x^2+2xy-24y^2[/tex]
There was a 2 in front of that multplicapltiation:
[tex]2(x+6y)(x-4y)[/tex]
[tex]2(x^2+2xy-24y^2)[/tex]
[tex]2x^2+4xy-48y^2[/tex]
This is exactly what we have on the left hand side of your given equation.
The factor of the trinomial 2x² + 4xy − 48y² will be2 (x − 4y)(x + 6y). Then the value of B will be 6.
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The trinomial is given below.
⇒ 2x² + 4xy − 48y²
Then the factor of the trinomial will be
⇒ 2x² + 12xy − 8xy − 48y²
⇒ 2x(x + 6y) − 8y (x + 6y)
⇒ (2x − 8y)(x + 6y)
⇒ 2 (x − 4y)(x + 6y)
Then the value of B will be 6.
More about the factorization link is given below.
https://brainly.com/question/6810544
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