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

the coefficient of B is, 9

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

Answer 2

The value of the coefficient B is 9.

2(x+By)(x-2y)
=2(x^2 -2xy +Bxy -2By^2)
=2x^2 -4xy + 2Bxy - 4By^2

The original form is 2x^2 + 14xy - 36y^2

-36y^2 = -4By^2
B= 9
-4xy +2Bxy= 14xy
xy(-4 +2B)= 14xy
-4 + 2B = 14
2B = 18
B=9