InterviewSolution
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InterviewSolution
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Simplify the following using the formula: (a-b)(a+b)=a2 - b2:(i) (82)2-(18)2(ii) (467)2-(33)2(iii) (79)2-(69)2(iv) 197 x 203(v) 113 x 87(vi) 95 x 105(vii) 1.8 x 2.2(viii) 9.8 x 10.2 |
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Answer» (i) (82)2- (18)2 Using formula: (a – b) (a + b) = a2 – b2, we get = (82 – 18) (82 + 18) = 64 × 100 = 6400 (ii) (467)2- (33)2 Using formula: (a – b) (a + b) = a2 – b2, we get = (467 – 33) (467 + 33) = (434) (500) = 217000 (iii) (79)2- (69)2 Using formula: (a – b) (a + b) = a2 – b2, we get = (79 + 69) (79 – 69) = (148) (10) = 1480 (iv) 197 x 203 Using formula: (a – b) (a + b) = a2 – b2, we get = (200 – 3) (200 + 3) = (200)2 – (3)2 = 40000 – 9 = 39991 (v) 113 x 87 Using formula: (a – b) (a + b) = a2 – b2, we get = (100 + 3) (100 – 3) = (100)2 – (3)2 = 10000 – 9 = 9991 (vi) 95 x 105 Using formula: (a – b) (a + b) = a2 – b2, we get = (100 – 5) (100 + 5) = (100)2 – (5)2 = 10000 – 25 = 9975 (vii) 1.8 x 2.2 Using formula: (a – b) (a + b) = a2 – b2, we get = (2- 0.2) (2 + 0.2) = (2)2 – (0.2)2 = 4 – 0.04 = 3.96 (viii) 9.8 x 10.2 Using formula: (a – b) (a + b) = a2 – b2, we get = (10 – 0.2) (10 + 0.2) = (10)2 - (0.2)2 = 100 – 0.04 = 90.96 |
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