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in Algebraic Expressions by (49.3k points)
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Using a2 – b2 = (a + b) (a – b), find

(i) 103 x 102
(ii) 7.1 x 7.3
(iii) 102 x 99
(iv) 9.8 x 9.6

1 Answer

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Best answer

(i) 103 x 102

= (100 + 3) x (100 + 2)

= (100)2 + (3 + 2) 100 + 3 x 2 (Using given identity)

= 10000 + 500 + 6

= 10506

(ii) 7.1 x 7.3

= (7 + 0.1) x (7 + 0.3)

= (7)2 + (0.1 + 0.3) 7 + (0.1) x (0.3) (Using given identity)

= 49 + 2.8 + 0.03

= 51.83

(iii) 102 x 99

= (100 + 2) x (100 – 1)

= (100 + 2) x {100 + (-1)}

= (100)2 + {2 + (- 1)} 100 + (2) (- 1) (Using given identity)

= 10000 + 100 – 2

= 10098

(iv) 9.8 x 9.6

= (10 – 0.2) x (10 – 0.4) .

= {10 + (-0.2)} x {10 +(-0.4)}

= (10)2 + {(- 0.2) + (- 0.4)} 10 + (- 0.2) (- 0.4) (Using given identity)

= 100 – 6 + 0.08

= 94.08

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