Question

evaluate 105 × 95 , using suitable identity

Answer 1

=105×95
=95×(100+5)
=95×100+95×5
=9500+475
=9975

Answer 2

The given data in the above question,

It is given that the value is (105 x 95)

Have to evaluate the given value by identity?

Thus, identity is comparing one equation with other we get,

$(105\times 95)=(100+5)(90+5)$

Comparing it with, $(a+b)(a-b)=a^{2}-b^{2}$

Further solving it we get,

$\begin{aligned}105 \times 95 &=(100+5)(100-5) \\&=(100)^{2}-(5)^{2} \\&=10000-25 \\&=9975\end{aligned}$

Hence we get the value as 9975.