Alg10.1

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Expand (2x+3y)^5\,

Applying the formula (x+y)^n=n \!C_0 x^n+n\!C_1 x^{n-1} y+n\!C_2 x^{n-2} y^2+......+n\!C_n y^n\, we get

(2x+3y)^5=5\!C_0 (2x)^5+5\!C_1 (2x)^4 (3y)+5\!C_2 (2x)^3 (3y)^2+5\!C_3 (2x)^2(3y)^3+5\!C_4(2x)^1 (5y)^4+5\!C_5 (5y)^5\,

(1)32x^5+5(16x^4)(3y)+\frac{5!}{3!2!}(8x^3)(9y^2)+\frac{5!}{2!3!}(4x^2)(27y^3)+\frac{5!}{1!4!} (2x)(625y^4)+1(3125y^5)\,

32x^5+240 x^4y+720 x^3 y^2+1080 x^2 y^3+6250 xy^4+3125 y^5\,


Wrong, correct is 32x^5+240 x^4y+720 x^3 y^2+1080 x^2 y^3+810 xy^4+243 y^5\,


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