Question

Simplify using the identities : $\frac{3.7\times 3.7-1.3\times 1.3}{3.7+1.3}$

Answer 1

Step 1 : Identify the identity we can use to simplify the question

If we take $a=3.7andb=1.3$, the we can clearly see the form of the identity .It is of the form ${\left(a\right)}^2-{\left(b\right)}^2$ which is equal to $(a+b)(a-b)$ in the numerator.

Step 2 : Simplify the given expression using the identity in the numerator

$\frac{3.7\times 3.7-1.3\times 1.3}{3.7+1.3}=\frac{{(3.7)}^2-{(1.3)}^2}{3.7+1.3}$

$=\frac{(3.7+1.3)(3.7-1.3)}{(3.7+1.3)}$

$=(3.7-1.3)[\mathrm{Cancelling}(3.7+1.3)\mathrm{from}\mathrm{numerator}\mathrm{and}\mathrm{denominator}]$

$=2.4$

Hence the result is $2.4$