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Using Binomial Theorem, Write Down the Expansions . (I) ( 2 X + 3 Y ) 5 - Mathematics

Using binomial theorem, write down the expansions  . 

(i)  \[\left( 2x + 3y \right)^5\]

 

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Solution

(i) (2x + 3y)

\[= ^{5}{}{C}_0 (2x )^5 (3y )^0 +^{5}{}{C}_1 (2x )^4 (3y )^1 + ^{5}{}{C}_2 (2x )^3 (3y )^2 +^{5}{}{C}_3 (2x )^2 (3y )^3 + ^{5}{}{C}_4 (2x )^1 (3y )^4 + ^{5}{}{C}_5 (2x )^0 (3y )^5\]  \[= 32 x^5 + 5 \times 16 x^4 \times 3y + 10 \times 8 x^3 \times 9 y^2 + 10 \times 4 x^2 \times 27 y^3 + 5 \times 2x \times 81 y^4 + 243 y^5 \]
\[ = 32 x^5 + 240 x^4 y + 720 x^3 y^2 + 1080 x^2 y^3 + 810x y^4 + 243 y^5 \] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.1 | Q 1.01 | Page 11
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