Simplify \(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
MATHEMATICS
WAEC 2003
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. \(\frac{3}{7}\)
Correct Answer: A. \(2\frac{1}{3}\)
Explanation
\(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2=\left(\frac{5}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
Difference of two squares
\(\left(\frac{5}{3}-\frac{2}{3}\right)\left(\frac{5}{3}+\frac{2}{3}\right)=\left(\frac{3}{3}\right)\left(\frac{7}{3}\right)\\
\frac{7}{3}=2\frac{1}{3}\)
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