InterviewSolution
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InterviewSolution
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Factorise the following using suitable identity.(i) x2 – 8x + 16(ii) y2 + 20y + 100(iii) 36m2 + 60m + 25(iv) 64x2 – 112xy + 49y2(v) a2 + 6ab + 9b2 – c2 |
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Answer» (i) x2 – 8x + 16 x2 – 8x + 16 = x2 – (2 x 4 (x) x) + 42 This expression is in the form of identity a2 – 2ab + b2 = (a – b)2 x2 – 2 (x) 4 (x) x + 42 = (x – 4)2 ∴ x2 – 8x + 16 = (x – 4) (x – 4) (ii) y2 + 20y + 100 y2 + 20y + 100 = y2 + (2 x (10)) y + (10 x 10) = y2 + (2 x 10 x y) + 102 This is of the form of identity a2 + 2 ab + b2 = (a + b)2 y2 + (2 x 10 x y) + 102 = (y + 10)2 y2 + 20y + 100 = (y + 10)2 y2 + 20y + 100 = (y + 10) (y + 10) (iii) 36m2 + 60m + 25 36m2 + 60m + 25 = 62 m2 + 2 x 6m x 5 + 52 This expression is of the form of identity a2 + 2ab + b2 = (a + b)2 (6m)2 + (2 x 6m x 5) + 52 = (6m + 5)2 36m2 + 60m + 25 = (6m + 5) (6m + 5) |
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