Question

Using identities, evaluate (a) 98² (b) 302 × 305 (c) 52 × 48 (d) 103²​

Answer 1

Step-by-step explanation:

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Using the identity (x+a)(x+b) = x

2

+(a+b)x+ab

Writing 102 as 100+2 and 98 as 100−2

Hence (100+2)(100−2) = 100

2

+[2+(−2)]100+(2)(−2)

= 10000+(0)100−4

= 9996

The answer is 9996

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Answer 2

Answer:

1.) (100-2) ^2

(a-b)^2= a^2-2ab+b^2

(100)^2-2×100×2+(2)^2

10000-400+4

9604

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2.) 302×305

(x+a)(x+b) =x^2+(a+b)x+ab

(300+2)(300+5)

(300)^2 + (2+5)300+2×5

90000 + 2100+10

920110

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3.) 52×48

(50+2)(50-2)

a^2-b^2 =(a+b)(a-b)

(50)^2-(2)^2

2500-4

2496

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4.) 103^2

(100+3)^2

(a+b)^2=a^2+2ab+b^2

(100)^2+2×100×3+(3)^2

10000+600+9

10609

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