How do you rewrite #3(x-5)+3x(x-5)# as an equivalent product of two binomials?

1 Answer
Jim G.
May 28, 2017

#3(x-5)(1+x)#

Explanation:

#color(red)(3)(x-5)color(red)(+3x)(x-5)#

#"take out the "color(blue)"common factor"" of " (x-5)#

#rArr(x-5)(color(red)(3+3x))#

#=(x-5)3(1+x)larr" common factor of 3 in " (3+3x)#

#=3(x-5)(1+x)#

#"we can check the 2 for equivalence"#

#3(x-5)+3x(x-5)#

#=3x-15+3x^2-15x#

#=3x^2-12x-15larrcolor(blue)" first expansion"#

#"and " 3(x-5)(1+x)larr" expand using FOIL"#

#=3(x+x^2-5-5x)#

#=3(x^2-4x-5)#

#=3x^2-12x-15larrcolor(blue)" second expansion"#

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