How do you factor #(x + y)^3 + (x - y)^3#?

2 Answers
Jun 5, 2018

Answer:

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

Explanation:

#(x+y)^3 + (x-y)^3#

Think about Pascal's Triangle to expand these terms:
# = (x^3 + 3xy^2 + 3x^2y + y^3) + (x^3 + 3xy^2 - 3x^2y - y^3)#

Combine like terms
# = 2x^3 + 6xy^2#

Factor:
# = (2x)(x^2+3y^2)#

Jun 5, 2018

Answer:

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

Explanation:

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

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

#"here "a=x+y" and "b=x-y#

#=(x+y+x-y)[(x+y)^2-(x+y)(x-y)+(x-y)^2]#

#=2x[x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2]#

#=2x(x^2+3y^2)#