Question

Given the trinomial, what is the value of the coefficient 'B' in the factored form?

Answer 1

Answer:

B=9  (I'll solve right now, just so you get the answer)

Step-by-step explanation:

$2x^2+14xy-36y^2=2(x+By)(x-2y)$

Expand right side by distributing

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

Use the FOIL method to simplify (first, outside, inside, last):

$(a+b)(c+d)=ac+ad+bc+bd$

$(2x*x)+(2x*(-2y))+(2By*x)+(2By*(-2y))$

Simplify

$2x^2-4xy+2Byx-4By^2$

Re-insert

$2x^2+14xy-36y^2=2x^2-4xy+2Byx-4By^2$

Cancel out $2x^2$

$14xy-36y^2=-4xy+2Byx-4By^2$

Move all terms to one side

$14xy-36y^2+4xy-2Byx+4By^2=0$

Simplify

$18xy-36y^2-2Byx+By^2=0$

Factor out the common term 2

$2(9xy-18y^2-Byx+2By^2)$