Solution 46 Page 18 Math Workbook 10 – Kite>


Topic

Determine the coefficient of \({x^4}\) in the expression expansion \({(2x + 3)^5}\)

Solution method – See details

Apply the expansion formula: \({(a + b)^5} = {a^5} + 5{a^4}b + 10{a^3}{b^2} + 10{a^2 }{b^3} + 5a{b^4} + {b^5}\) with \(a = 2x,b = 3\)

Detailed explanation

We have: \({(2x + 3)^5} = {(2x)^5} + 5. {(2x)^4}.3 + 10. {(2x)^3}{.3^2} + 10. {(2x)^2}{.3^3} + 5.2x{.3^4} + {3^5}\)

\( = 32{x^5} + 240{x^4} + 720{x^3} + 1080{x^2} + 810x + 243\)

The term containing \({x^4}\) in the expression expansion \({(2x + 3)^5}\) is \(240{x^4}\)

So the coefficient of \({x^4}\) in the expression expansion \({(2x + 3)^5}\) is 240



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