Question

If $(a+b{)}^2=64$ and $ab=12$. What is the value of $(a-b{)}^2$?

• A. 112
• B. 16
• C. 64
• D. 48

Answer 1

The correct option is B

16

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

$=2ab+2ab=4ab$

So, $(a-b{)}^2=(a+b{)}^2-4ab$

Substituting the values we get:

$=(a-b{)}^2=64-4\times 12=64-48=16$