y = (1/3)(3x + 4)^3
y’ = 27x^2 + 72x + 48
To expand the expression y = (1/3)(3x + 4)^3, we can begin by applying the binomial expansion formula. This formula is given by:
(a + b)^n = nC0(a^n)b^0 + nC1(a^n-1)b^1 + nC2(a^n-2)b^2 + … + nCn(a^0)b^n
Where nCi is the binomial coefficient, given by n!/(i!(n-i)!).
Using this formula, we can write:
(3x + 4)^3 = 3C0(3x)^3 4^0 + 3C1(3x)^2 4^1 + 3C2(3x)^1 4^2 + 3C3(3x)^0 4^3
Simplifying this expression, we get:
(3x + 4)^3 = 27x^3 + 108x^2 + 144x + 64
Now we can substitute this expression back into the original equation:
y = (1/3)(27x^3 + 108x^2 + 144x + 64)
Expanding the expression further, we get:
y = 9x^3 + 36x^2 + 48x + 21.333
Therefore, the expanded form of y = (1/3)(3x + 4)^3 is y = 9x^3 + 36x^2 + 48x + 21.333.
More Answers:
[next_post_link]