Question

Which of the following is correct?

• A. ${(a–b)}^2=a^2+2ab–b^2$
• B. ${(a–b)}^2=a^2–2ab+b^2$
• C. ${(a–b)}^2=a^2–b^2$
• D. ${(a+b)}^2=a^2+2ab–b^2$

Answer 1

The correct option is B

${(a–b)}^2=a^2–2ab+b^2$

Determine the correct choice.

${(a–b)}^2=a^2–2ab+b^2$

We have,

$\begin{array}{rcl}(a–b)\times (a–b)& =& a\times (a–b)–b\times (a–b)\\ & =& a^2–ab–ba+b^2\\ & =& a^2–2ab+b^2\end{array}$

Hence, the correct choice is "Option B".