What is the second term of (2x 2 ‑ 3y)^6 ? Your answer should be in the form (sign)(numerical factors)(actual powers of variables).

Respuesta :

Answer:

[tex]-6(2^5)(3)x^{10}y[/tex].

Step-by-step explanation:

Use the binomial theorem: given any variables a,b and a positive integer n, [tex](a+b)^n=\sum_{k=0}^n \binom{n}{k}a^{n-k}b^{k}[/tex].

In this case, take [tex]a=2x^2,b=-3y,n=6[/tex]

Usually, the terms on a polynomial of two variables are ordered starting with the highest power of x (x^12 in this case) and the lowest power of y. The powers of x decrease and the powers of y increase, so the last term has the highest power of y and the lowest power of x .

Then, the second term is k=1 as it has the second highest power of x, so replacing these values this term is:

[tex]\binom{6}{1}(2x^2)^5 (-3y)^{1}=6(2^5 x^{10})(-3y)=-6(2^5)(3)x^{10}y[/tex].

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