Question

$(a+b{)}^3-(a-b{)}^3$is always divisible by

• A. 3
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is B

2

$(a+b{)}^3=a^3+3a^{2}b+3a{b}^2+b^3$
$(a-b{)}^3=a^3-3a^{2}b+3a{b}^2-b^3$
$(a+b{)}^3-(a-b{)}^3=2(3a^{2}b+b^3)$
This is always divisible by 2.