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

First factor out the 2 to get:\[\bf \implies 2(x^2+7xy-18y^2)=2(x+By)(x-2y)\]Dividng both sides by 2 yields:\[\bf \implies x^2+7xy-18y^2=(x+By)(x-2y)\]Now expand the right hand side (expand the factored equation):\[\bf \implies x^2+7xy-18y^2=x^2-2xy+Bxy-2By^2\]Now let's factor out the 'xy' from the second and third terms:\[\bf \implies x^2+7xy-18y^2=x^2+ (B-2)xy-2By^2\]Now let's compare coefficients; We know that that the right and left quadratics are both identical hence the coefficient of \(\bf xy\) must be the same in both. This then implies:\[\bf B-2=7 \implies B = 9\]Similarly, you could also compare the coefficients of \(\bf y^2\) in both quadratic which also yields the same answer:\[\bf 2B=18 \implies B = 9\]

Answer 2

@Nitotheburito

Answer 3

$$2x^2+14xy-36y^2=\frac{(2x+18y) (2x-4y)}{2}=\frac{2(x+9y)2(x-2y)}{2}=2(x+9y)(x-2y)$$

Answer 4

Thank you for breakin it down

Answer 5

@genius12

Answer 6

i just did this for hmwk. the answer is 2