Question

Find ${107}^2-{75}^2$.

• A. $17000$
• B. $17225$
• C. $17245$
• D. $17074$

Answer 1

The correct option is D $17074$

75 ends with 5 so the last two digits will be 25 (_ _ 25)
The first two digits can be found as $7\times 8=56$
So, ${75}^2=5625$

${107}^2=(100+7)\times (100+7)$
${107}^2=(100\times 100)+(100\times 7)+(7\times 100)+(7\times 7)$
${107}^2=10000+700+700+49$
${107}^2=11449$

$⟹{75}^2+{107}^2=11449+5625$
${75}^2+{107}^2=17074$