Question

Which of the following is an expansion of the identity ${(a–b)}^3$?

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

Answer 1

The correct option is C $a^3-b^3-3a^{2}b+3a{b}^2$

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