Question

(2x3 + 3y2)7 binomial expansion

Answer 1

42+42y=0
42=-42y
42/-42=y
-1=y

Answer 2

$\textbf {Hey there, here is the solution.}$

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Using the pascal triangle method, we know that a binomial with a power of y expand to this:

$(x+y)^7 = x^7 + 7x^6y + 21x^5y2^2 + 35x^4y^3 + 35x^3y^4 + 21x^2y^5 + yxy^6 + y^7$

.

Hence, applying the expansion to (x³ + 3y²)⁷:

$(2x^3+3y^2)^7 = (2x^3)^7 + 7(2x^3)^6(3y^2) + 21(2x^3)^5(3y^2)^2 + 35(2x^3)^4(3y^2)^3 + 35(2x^3)^3(3y^2)^4 + 21(2x^3)^2(3y^2)^5 + (2x^3)^6(3y^2) + (3y^2)^7$

$(2x^3+3y^2)^7 = 128x^{21} + 1344x^{18}y^2 + 6048x^{15}y^4 + 15120x^{12}y^6 + 2260x^9y^8 + 20412x^6y^{10} + 10206x^3y^{12} + 2187y^4$

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* Attached here is the pascal triangle for your reference on the coefficients used.

$\textbf {Cheers}$