Answer:
B=9 (I'll solve right now, just so you get the answer)
Step-by-step explanation:
[tex]2x^2+14xy-36y^2=2(x+By)(x-2y)[/tex]
Expand right side by distributing
[tex](2x+2By)(x-2y)[/tex]
Use the FOIL method to simplify (first, outside, inside, last):
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
[tex](2x*x)+(2x*(-2y))+(2By*x)+(2By*(-2y))\\\\[/tex]
Simplify
[tex]2x^2-4xy+2Byx-4By^2[/tex]
Re-insert
[tex]2x^2+14xy-36y^2=2x^2-4xy+2Byx-4By^2[/tex]
Cancel out [tex]2x^2[/tex]
[tex]14xy-36y^2=-4xy+2Byx-4By^2[/tex]
Move all terms to one side
[tex]14xy-36y^2+4xy-2Byx+4By^2=0[/tex]
Simplify
[tex]18xy-36y^2-2Byx+By^2=0[/tex]
Factor out the common term 2
[tex]2(9xy-18y^2-Byx+2By^2)[/tex]
