Question

Which of the following is a factor of (x+y)³ - (x³+y³) ?

choose the correct answer
x²+xy²+2xy

x²+y²-xy

xy²

3xy


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Answer 1

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

Thus,

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

= 3x^2y + 3xy^2

= 3xy(x + y)

Hence, 3xy(x+y) is the simplest factorisation form for (x+y)³ - (x³+y³).

Answer 2

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

Thus,

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

= 3x^2y + 3xy^2

= 3xy(x + y)

Hence, 3xy(x+y) is factor of (x+y)³ - (x³+y³).