Question

The value of (107)${}^2$ - (93)${}^2$ is: ____.

• A. 1382
• B. 36482
• C. 1008
• D. 2800

Answer 1

The correct option is D 2800

(107)${}^2$ can be written as (100+7)${}^2$ and (93)${}^2$ can be written as (100-7)${}^2$.
${107}^2-{93}^2=(100+7{)}^2-(100-7{)}^2$.
This is in the form of $(a+b{)}^2-(a-b{)}^2$ where a = 100 and b=7

We know that, $(a+b{)}^2=a^2+2ab+b^2$ and $(a-b{)}^2=a^2-2ab+b^2$
$(a+b{)}^2-(a-b{)}^2=a^2+2ab+b^2-a^2-2ab+b^2=4ab$
${107}^2-{93}^2=4ab=4\times 100\times 7=2800$