How do you factor # 14x^2+23xy+3y^2#?

1 Answer
Jun 11, 2018

Answer:

#(2x+3y)(7x+y)#

Explanation:

#"although the quadratic has 2 variables we deal with it"#
#"in the same manner as one variable quadratics"#

#"using the a-c method to factor"#

#"the factors of the product "14xx3=42#

#"which sum to + 23 are + 21 and + 2"#

#"split the middle term using these factors"#

#14x^2+21xy+2xy+3y^2larrcolor(blue)"factor by grouping"#

#=color(red)(7x)(2x+3y)color(red)(+y)(2x+3y)#

#"take out the "color(blue)"common factor "(2x+3y)#

#=(2x+3y)(color(red)(7x+y))#

#14x^2+23xy+3y^2=(2x+3y)(7x+y)#