Question

Find the cube of 3a - 2b .

• A. $27a^3-8b^3-54a^{2}b+36a{b}^2$
• B. $27a^3-54b^3-8a^{2}b+36a{b}^2$
• C. $27a^3+8b^3+54a^{2}b+36a{b}^2$
• D. $27a^3-8b^3-54a^{2}b-36a{b}^2$

Answer 1

The correct option is A $27a^3-8b^3-54a^{2}b+36a{b}^2$

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

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

= $(3a{)}^3-(2b{)}^3-18ab(3a-2b)$

= $27a^3-8b^3-54a^{2}b+36a{b}^2$