InterviewSolution
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InterviewSolution
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Solve the question Algebraic Expressions(i) (a2 − b2)2 (ii) (2x +5)2 − (2x − 5)2(iii) (7m − 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2 |
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Answer» (i) (a2 − b2)2 = (a2)2 − 2(a2) (b2) + (b2)2 [(a − b)2 = a2 − 2ab + b2 ] = a4 − 2a2b2 + b4 (ii) (2x +5)2 − (2x − 5)2 = (2x)2 + 2(2x) (5) + (5)2 − [(2x)2 − 2(2x) (5) + (5)2] [(a − b)2 = a2 − 2ab + b2] [(a + b)2 = a2 + 2ab + b2] = 4x2 + 20x + 25 − [4x2 − 20x + 25] = 4x2 + 20x + 25 − 4x2 + 20x − 25 = 40x (iii) (7m − 8n)2 + (7m + 8n)2 = (7m)2 − 2(7m) (8n) + (8n)2 + (7m)2 + 2(7m) (8n) + (8n)2 [(a − b)2 = a2 − 2ab + b2 and (a + b)2 = a2 + 2ab + b2] = 49m2 − 112mn + 64n2 + 49m2 + 112mn + 64n2 = 98m2 + 128n2 (iv) (4m + 5n)2 + (5m + 4n)2 = (4m)2 + 2(4m) (5n) + (5n)2 + (5m)2 + 2(5m) (4n) + (4n)2 [ (a + b)2 = a2 + 2ab + b2] = 16m2 + 40mn + 25n2 + 25m2 + 40mn + 16n2 = 41m2 + 80mn + 41n2 |
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