InterviewSolution
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InterviewSolution
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Simplify(i) (a2 – b2)2(ii) (2n + 5)2 – (2n – 5)2(iii) (7m – 8n)2 + (7m + 8n)2(iv) (m2 – n2m)2 + 2m3n2 |
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Answer» (i) (a2 – b2)2 = (a2)2 – 2(a2) (b2) + (b2)2 (Using identity II) = a4 – 2a2b2 + b4 (ii) (2n + 5)2 – (2n – 5)2 = {(2n)2 + 2 (2n) (5) + (5)2} – {(2n)2 – 2(2n) (5) + (5)2} = (4n2 + 20n + 25) – (4n2 – 20n + 25) = 4n2 + 20n + 25 – 4n2 + 20n – 25 = 4n2 – 4n2 + 20n + 20n + 25 – 25 = 0 + 40n + 0 = 40n Alternative Method- (2n + 5)2 – (2n – 5)2 = {(2n + 5) + (2n – 5)} {(2n + 5) – (2n – 5)} = (4n) (10) = 40n (iii) (7m – 8n)2 + (7m + 8n)2 = {(7m)2 – 2(7m) (8n) + (8n)2} + {(7m)2 + 2(7m) (8n) + (8n)2} (Using identity I and II) = (49m2 – 112mn + 64n2) + (49m2 + 112mn + 64n2) = 49m2 – 112mn + 64n2 + 49m2 + 112 mn + 64 n2 = 49m2 + 49m2 – 112mn + 112mn + 64m2 + 64n2 = 98m2 + 128n2 (iv) (m2 – n2m)2 + 2m3n2 = [(m2)2 – 2(m2) (n2m) + (n2m)2] + 2m3n2 (Using identity II) = m4 – 2m3n2 + n4m2 + 2m3n2 = m4 – 2m3n2 + 2m3n2 + n4m2 = m + n4m2 |
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