Question
Simplify the following using the identities:
$\frac{8.63×8.63−1.37\times1.37}{0.726}$
$\frac{8.63×8.63−1.37\times1.37}{0.726}$
✓
Answer
Let us consider the following expression:$\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{8.63^2−1.37^2}{0.726}$
Using the identity $(a+b)(a-b)=a^2-b^2$ $\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{8.63^2−1.37^2}{0.726}\\=\frac{(8.63+1.37)(8.63−1.37)}{0.726}$
$\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{(8.63+1.37)(8.63−1.37)}{0.726}$
$\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{10×7.26}{0.726}$
$\frac{8.63×8.63−1.37×1.37}{0.726}=100$
Thus, the answer is 100.
Using the identity $(a+b)(a-b)=a^2-b^2$ $\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{8.63^2−1.37^2}{0.726}\\=\frac{(8.63+1.37)(8.63−1.37)}{0.726}$
$\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{(8.63+1.37)(8.63−1.37)}{0.726}$
$\frac{8.63×8.63−1.37\times1.37}{0.726}=\frac{10×7.26}{0.726}$
$\frac{8.63×8.63−1.37×1.37}{0.726}=100$
Thus, the answer is 100.
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