Using identities- evaluate 95 - 105-

The correct option is B 997595 can be written as 100 5 and 105 can be written as 100+ 5. 95 × 105 = nbsp; nbsp;(100 5) × (100+ 5) which is in the form ...

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Standard VIII

Mathematics

Algebraic Identity: (a - b)(a + b) = a^2 - b^2

Using identit...

Question

Using identities, evaluate 95 $\times$ 105.

9999

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9975

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9925

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9950

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Solution

The correct option is B 9975
95 can be written as 100 - 5 and 105 can be written as 100+ 5.
$95 \times 105 = (100 - 5) \times (100 + 5)$ which is in the form $(a - b) (a + b)$ where a = 100 and b = 5.

We know that, $(a - b) (a + b) = a^{2} - b^{2}$
$95 \times 105 = (100 - 5) (100 + 5) = 100^{2} - 5^{2}$
$= 10000 - 25$
$= 9975$

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Using identities, evaluate 95 × 105.

The correct option is B 997595 can be written as 100 - 5 and 105 can be written as 100+ 5. 95×105=(100−5)×(100+5) which is in the form (a−b)(a+b) where a = 100 and b = 5. We know that,(a−b)(a+b)=a2−b2 95×105=(100−5)(100+5)=1002−52 =10000−25 =9975

Using identities, evaluate 95 $\times$ 105.