Question

rewrite the following expression in expanded form and simplify completely.

\\(3x - y)^4\\

Explanation:

Apply the Binomial Theorem formula

$$ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k $$

$$ a = 3x, \quad b = -y, \quad n = 4 $$

Expand the terms using binomial coefficients

$$ \binom{4}{0}(3x)^4(-y)^0 + \binom{4}{1}(3x)^3(-y)^1 + \binom{4}{2}(3x)^2(-y)^2 + \binom{4}{3}(3x)^1(-y)^3 + \binom{4}{4}(3x)^0(-y)^4 $$

$$ 1(81x^4)(1) + 4(27x^3)(-y) + 6(9x^2)(y^2) + 4(3x)(-y^3) + 1(1)(y^4) $$

Simplify the expanded expression

$$ 81x^4 - 108x^3y + 54x^2y^2 - 12xy^3 + y^4 $$

Answer:

Rewrite the following expression in expanded form and simplify completely.

$$(3x - y)^4 =$$

<blank>\(81x^4 - 108x^3y + 54x^2y^2 - 12xy^3 + y^4\)</blank>