Simplify \(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
A
\(2\frac{1}{3}\)
B
\(1\frac{1}{3}\)
C
1
D
\(\frac{3}{7}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2=\left(\frac{5}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
Difference of two squares
\(\left(\frac{5}{3}-\frac{2}{3}\right)\left(\frac{5}{3}+\frac{2}{3}\right)=\left(\frac{3}{3}\right)\left(\frac{7}{3}\right)\\
\frac{7}{3}=2\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #26580)