How do you factor #8m^3 - 125n^3#?

2 Answers
May 16, 2018

Answer:

#(2m-5n)(4m^2+10mn+25n^2)#

Explanation:

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

#"and factors in general as"#

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

#8m^3=(2m)^3rArra=2m#

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

#8m^3-125n^3=(2m-5n)((2m)^2+(2mxx5n)+(5n)^2)#

#color(white)(xxxxxxxxx)=(2m-5n)(4m^2+10mn+25n^2)#

May 16, 2018

Answer:

#(2m-5n) (4m^2 + 10mn + 25n^2)#

Explanation:

Remember that #a^3-b^3=(a-b)(a^2+ab+b^2)#

#8m^3-125n^3=2^3m^3-5^3n^3=(2m)^3-(5n)^3#

Therefore, #a=2m, b=5n#

Sub in: #(2m-5n) (4m^2 + 10mn + 25n^2)#