Question

c
2. Using identities, find the value of :
(a) 102 x 103 (b) 52 x 47
(c) 98 X 97
(d) (39)
(e) (54)
(f) (78)
(g) (999)
(h) (103)
(i) (7.5)?
3. Using identities, find th , valui, of:
(a) (72)2 – (18)
(b) (138)2 – (62)
(c) 194 x 206
(d) 161 x 161 - 61 x 61
A.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

2.

(a)

$102 \times 103 \\ = (100 + 2)(100 + 3) \: \: \: using \: \: \: (x + a)(x + b) = {x}^{2} + (a + b)x + ab\\ = {100}^{2} + (2 + 3)100 + 6 \\ = 10000 + (5)100 + 6 \\ = 10000 + 500 + 6 \\ = 10506$

(b)

$52\times47 \\=(50+2)(50-3)\\{50}^{2} + (2 + (-3))50 + (-6) \\ = 2500 + (-1)50 - 6 \\ = 2500 - 50 - 6 \\ = 2444$

(c)

$98\times97 \\=(100-2)(100-3)\\{100}^{2} + (-2 + (-3))100 + (6) \\ = 10000 + (-5)100 + 6 \\ = 10000 - 500 + 6 \\ = 9506$