Solve ${(2 x + 3 y)}^{5}$ using binomial theorem

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Solution

Let us solve the given expressionusing binomial theorm
${(2 x + 3 y)}^{5} = 5 C_{0} {(2 x)}^{5} {(3 y)}^{0} + 5 C_{1} {(2 x)}^{4} {(3 y)}^{1} + 5 C_{2} {(2 x)}^{3} {(3 y)}^{2} + 5 C_{3} {(2 x)}^{2} {(3 y)}^{3} + 5 C_{4} {(2 x)}^{1} {(3 y)}^{4} + 5 C_{5} {(2 x)}^{0} {(3 y)}^{5} = 32 x^{5} + 5 (16 x^{4}) (3 y) + 10 (8 x^{3}) (9 y^{2}) + 10 (4 x^{2}) (27 y^{3}) + 5 (2 x) (81 y^{4}) + 243 y^{5} = 32 x^{5} + 240 x^{4} y + 720 x^{3} y^{2} + 1080 x^{2} y^{3} + 810 x y^{4} + 243 y^{5}$

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