Use the formula to find the values.

(i) 502 × 498 (ii) 97 × 103 (iii) 54 × 46 (iv) 98 × 102

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Solution

It is known that, (a + b) (a − b) = a² − b².

(i) 502 × 498
= (500 + 2) × (500 − 2)
= (500)² − (2)²
= 250000 − 4
= 249996

(ii) 97 × 103
= (100 − 3) × (100 + 3)
= (100)² − (3)²
= 10000 − 9
= 9991

(iii) 54 × 46
= (50 + 4) × (50 − 4)
= (50)² − (4)²
= 2500 − 16
= 2484

(iv) 98 × 102
= (100 − 2) × (100 + 2)
= (100)² − (2)²
= 10000 − 4
= 9996

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Similar questions

Evaluate:

(i) 53 × 55; (ii) 102 × 106; (iii) 34 × 36; (iv) 103 × 96.

(x + a) (x + b) = x^{2} + (a + b) x + a b

103 \times 104

5.1 \times 5.2

103 \times 98

9.7 \times 9.8

Using the formula for squaring a binominal evaluate the following:
(i) $(54)^{2}$
(ii) $(82)^{2}$
(iii) $(103)^{2}$
(iv) $(704)^{2}$

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