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Binomial Theorem Exercises With AnswersWe Do Not Need To Fully Expand A Binomial To Find A Single Specific Term. Note The Pattern Of Coefficients In The Expansion Of \({(x+y)}^5\). \({(x+y)}^5=x^5+\dbinom{5}{1}x^4y+\dbinom{5} {2}x^3y^2+\dbinom{5}{3}x^2y^3+\dbinom{5}{4}xy^4+y^5\) The Second Term Is \(\dbinom{5}{1}x^4y\). The Third Term Is \ Mar 16th, 2024Binomial Theorem Examples With FractionsThen Using The Binomial Theorem, We HaveFinally (x2 - 2y)5 = X10 - 10x8y + 40x6y2 - 80x4y3 + 80x2y4 - 32y5. Example 4 Expand: (2/x + 3√x)4. Solution We Have (a + B)n, Where A = 2/x, B = 3√x, And N = 4. Then Using The B Mar 7th, 20241 Binomial TheoremThere Is No Need To Expand Either Binomial Beyond X4 As Those Terms Will Not Contribute To The Coe¢ Cient Of X4. The Exist Only Two Ways To Achieve An X4 Term In Our Expansion: A Cubic Term From 4 X3 5 And A Linear Term From (2x+3)7 Or A Constant Term From 4 X3 5 And An X4 Term From (2x+3)7. Thus, The Coe¢ Jan 1th, 2024.
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