Question

using suitable identities evaluate the following 105×95​

Answer 1

Required Answer:-

$\sf \color{darkblue}105 \times 95 \\ = (100 + 5)(100 - 5) \\ = (100) {}^{2} - (5) {}^{2} \\ \tt \color{blue}\therefore(a + b)(a - b) = a {}^{2} - b {}^{2} \\ = 1000 0 - 25 \\ \color{orange} = 9975$

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Know More:-

• Identity I: (a + b)² = a²+ ²ab + b²
• Identity III: a² – b²= (a + b)(a – b)
• Identity IV: (x + a)(x + b) = x²+ (a + b) x + ab.
• Identity V: (a + b + c)² = a² + b² + c²+ 2ab + 2bc + 2ca.
• Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)

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Answer 2

As per the data given in the above question.

In the above question, it is given that,

The given data is $105\times 95$,

To evaluate the given value by identities,

Thus, identities is to compare one equation with other we get,

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

compare, $(a+b)(a-b)=a^{2}-b^{2}$

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.