Question

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

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

B= ____________

Answer 1

Took the test and got it right

Answer 2

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

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)`