Question

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

Answer 1

Answer:

$-6(2^5)(3)x^{10}y$.

Step-by-step explanation:

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

In this case, take $a=2x^2,b=-3y,n=6$

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:

$\binom{6}{1}(2x^2)^5 (-3y)^{1}=6(2^5 x^{10})(-3y)=-6(2^5)(3)x^{10}y$.