Simplify
\[ \frac{7.83 \times 7.83 – 1.17 \times 1.17}{6.66} \]
Solution:
Using identity:
\[ a^2 – b^2 = (a-b)(a+b) \]
\[ \frac{(7.83)^2 – (1.17)^2}{6.66} \]
\[ = \frac{(7.83 – 1.17)(7.83 + 1.17)}{6.66} \]
\[ = \frac{(6.66)(9)}{6.66} \]
\[ = 9 \]
\[ \frac{7.83 \times 7.83 – 1.17 \times 1.17}{6.66} \]
Using identity:
\[ a^2 – b^2 = (a-b)(a+b) \]
\[ \frac{(7.83)^2 – (1.17)^2}{6.66} \]
\[ = \frac{(7.83 – 1.17)(7.83 + 1.17)}{6.66} \]
\[ = \frac{(6.66)(9)}{6.66} \]
\[ = 9 \]