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What is the coefficient of x^2y^2 in (x + 1)^2 . (x + 1)^3?(a) 1(b) 5(c) 2(d) 10This question was posed to me during an internship interview.I'm obligated to ask this question of Binomial Theorem for Positive Integral Index topic in division Binomial Theorem of Mathematics – Class 11 |
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Answer» CORRECT answer is (a) 1 The best I can EXPLAIN: We KNOW that (a + B)^2 = a^2 + 2ab + b^2 (a + b)^3 = a^3 + 3ab^2 + 3a^2b + b^2 Using these formulae, we get P(x) = (x^2 + 2XY + y^2)(x^3 + 3xy^2 + 3x^2y + y^2) P(x) = 3xy^4 + 9x^2y^3 + 10x^3y^2 + 5x^4y + x^5 + y^4 + 2xy^3 + x^2y^2 The coefficient of x^2y^2 in (x + 1)^2 . (x + 1)^3 is 1. |
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