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