Answer:
the coefficient of B is, 9
Step-by-step explanation:
Given the trinomial:
[tex]2x^2+14xy-36y^2 = 2(x+By)(x-2y)[/tex]
First Multiply:
[tex]2(x+By)(x-2y)[/tex]
Distribute the first term of the first expression to the second expression and second term of the first expression to the second expression
⇒[tex]2(x^2-2xy+Bxy-2By^2)[/tex]
⇒[tex]2x^2-4xy+2Bxy-4By^2[/tex]
⇒[tex]2x^2+xy(-4+2B)-4By^2[/tex]
Now;
[tex]2x^2+14xy-36y^2 = 2x^2+xy(-4+2B)-4By^2[/tex]
On comparing both sides we have;
[tex]-4+2B = 14[/tex]
Add 4 to both sides we have;
[tex]2B = 18[/tex]
Divide both sides by 2 we have;
B =9
or
-4B = -36
Divide both side by -4 we have;
B = 9
Therefore, the coefficient of B is, 9
