the no. terms in the expansion of (x+a)^100+(x-a)^100 after simplification is:
Answers
Total number of terms = 51 in the expansion of (x + a)¹⁰⁰ + (x - a)¹⁰⁰
Step-by-step explanation:
(x + a)¹⁰⁰ + (x - a)¹⁰⁰
(x + a)¹⁰⁰ = x¹⁰⁰ + ¹⁰⁰C₁x¹⁰⁰⁻¹a¹ +...........+ ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿaⁿ +.................¹⁰⁰C₁₀₀x⁰a¹⁰⁰
(x - a)¹⁰⁰ = x¹⁰⁰ + ¹⁰⁰C₁x¹⁰⁰⁻¹(-a)¹ +..........+ ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿ(-a)ⁿ +...............¹⁰⁰C₁₀₀x⁰(-)a¹⁰⁰
Adding Both ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿaⁿ + ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿ(-a)ⁿ = 0 for n = odd
n = 1 , 3 , 5 ..................................., 97 , 99 = 50 Terms
¹⁰⁰Cₙ x¹⁰⁰⁻ⁿaⁿ + ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿ(-a)ⁿ = 2 ¹⁰⁰Cₙ x¹⁰⁰⁻ⁿaⁿ for n = Even
n = 0 , 2 , 4 , .................................., 98 , 100 = 51 Terms
(x + a)¹⁰⁰ + (x - a)¹⁰⁰ = 2(x¹⁰⁰ + ¹⁰⁰C₂x¹⁰⁰⁻²a² +...........+ ¹⁰⁰C₂ₙ x¹⁰⁰⁻²ⁿa²ⁿ +.................¹⁰⁰C₁₀₀x⁰a¹⁰⁰)
Total number of terms = 51
Total number of terms = 51 in the expansion of (x + a)¹⁰⁰ + (x - a)¹⁰⁰
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