How do you factor #27r^3 + 125s^3#?

2 Answers
Jim G.
May 14, 2018

#3r+5s)(9r^2-15rs+25s^2)#

Explanation:

#"this is a "color(blue)"sum of cubes"#

#"which factors in general as"#

#•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)#

#27r^3=(3r)^3rArra=3r#

#125s^3=(5s)^3rArrb=5s#

#rArr27r^3+125s^3#

#=(3r+5s)((3r)^2-(3rxx5s)+(5s)^2)#

#=(3r+5s)(9r^2-15rs+25s^2)#

James
May 14, 2018

#(3r+5s)*(9r^2-15rs+25s^2)#

Explanation:

show below

#27r^3 + 125s^3#

#(3r)^3+(5s)^3#

#(3r+5s)*(9r^2-15rs+25s^2)#

Note that

#x^3+y^3#

#(x+y)(x^2-xy+y^2)#

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