Question 86 (viii)

Using suitable identities, evaluate the following:

$52 \times 53$

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Solution

We have,
$52 \times 53 = (50 + 2) (50 + 3) = (50)^{2} + (2 + 3) 50 + 2 \times 3$
[using the identity, $(x + a) (x + b) = x^{2} + (a + b) x + a b$ ]
$= 2500 + 250 + 6 = 2756$

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