How do you factor the expression #2x^2 + 13xy +15y^2#?

1 Answer
Mar 19, 2016

(2x + 3y)(x + 5y)

Explanation:

Consider y as a constant. factor the quadratic trinomial for x.
Use the new AC Method to factor trinomial.
#f(x) = 2x^2 + 13xy + 15y^2 =# 2(x + p)(x + q)
Converted trinomial #f'(x) = x^2 + 13xy + 30y^2 =# (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of #(ac = 30y^2)# --> (2y, 15y)(3y, 10y) . This sum is
13y = b. Then, p' = 3y and q' = 10y.
Back to original trinomial: #p = (p')/a = (3y)/2#, and
#q = (q')/a = 10y/2 = 5y.#
Factored form:
#y = 2(x + 3y/2)(x + 5y) = (2x + 3y)(x + 5y)#