Answer :
The coefficient of x^7 in the expansion of (3x^2)^10 is 10.
What is Binomial theorem?
An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.
The binomial theorem states that for any two numbers a and b, and for any positive integer n, the expansion of (a + b)^n is given by:
[tex](a + b)^n = a^n + na^(n-1)b + n(n-1)/2a^(n-2)*b^2 + ... + b^n[/tex]
In this case, we want to find the coefficient of x^7 when the expression [tex](3x^2)^10[/tex] is expanded using the binomial theorem.
Substituting the values a = 3x^2 and b = 1 into the formula above, we get:
[tex](3x^2 + 1)^10 = 3x^2^10 + 103x^2^91 + 453x^2^81^2 + ... + 1^10[/tex]
The coefficient of x^7 in this expansion is given by the term [tex]103x^2^91.[/tex]To find the coefficient, we can ignore the [tex]x^2^9[/tex] and 1 terms, and just focus on the coefficient of 10.
Therefore, The coefficient of x^7 in the expansion of (3x^2)^10 is 10.
To know more about binomial theorem visit,
https://brainly.com/question/13672615
#SPJ4
