Question

Cube of $a-2b$ is _______.

• A. $a^3-8b^3-6a^{2}b+12a{b}^2$
• B. $a^3+8b^3-6a^{2}b+12a{b}^2$
• C. $8a^3-18b^3-6a^{2}b+12a{b}^2$
• D. $a^3+8b^3+6a^{2}b+12a{b}^2$

Answer 1

The correct option is A $a^3-8b^3-6a^{2}b+12a{b}^2$

Using the identity,

$(a-b{)}^3=a^3-b^3-3ab(a-b)$,

$(a-2b{)}^3$

= $(a{)}^3-(2b{)}^3-3\times a\times 2b(a-2b)$

= $(a{)}^3-(2b{)}^3-6ab(a-2b)$

= $a^3-8b^3-6a^{2}b+12a{b}^2$