How do you factor #r^ { 2} + 12r z + 27z ^ { 2}#?

2 Answers
YamDeeYoumar
Jun 16, 2018

Splitting middle term,

#r^2+3rz+9rz+27z^2#

#r(r+3z)+9z(r+3z)#

#r+9z (r+3z)#

Jim G.
Jun 16, 2018

#(r+3z)(r+9z)#

Explanation:

#"we can factor a quadratic with 2 variables in the same"#
#"way we factor a quadratic in one variable"#

#"using the a-c method of factoring a quadratic"#

#"the factors of the product "1xx27=27#

#"which sum to + 12 are + 3 and + 9"#

#"split the middle term using these factors"#

#r^2+3rz+9rz+27z^2larrcolor(blue)"factor by grouping"#

#=color(red)(r)(r+3z)color(red)(+9z)(r+3z)#

#"take out the "color(blue)"common factor "(r+3z)#

#=(r+3z)(color(red)(r+9z))#

#r^2+12rz+27z^2=(r+3z)(r+9z)#

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