Use Binomial Expansion to expand:

(3𝑥 − 5)^4

would this be the final answer using Binomial Expansion?

81x^4-540x^3+1350x^2-1500x+625

correct

Tu respuesta es correcta

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dang it

busted already

To expand (3𝑥 − 5)^4 using the Binomial Expansion formula, you can apply the binomial coefficients and exponents to the terms within the equation.

The Binomial Expansion formula for an expression (a + b)^n is:
(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, k)a^(n-k) b^k + ... + C(n, n)a^0 b^n

In our case, a is 3𝑥 and b is -5, and n is 4. Using this information, we can substitute these values into the formula to expand (3𝑥 − 5)^4.

So let's calculate each term one by one:

Term 1: C(4,0)(3𝑥)^4 (-5)^0 = 1(3𝑥)^4 = 81𝑥^4

Term 2: C(4,1)(3𝑥)^3 (-5)^1 = 4(3𝑥)^3 (-5) = -540𝑥^3

Term 3: C(4,2)(3𝑥)^2 (-5)^2 = 6(3𝑥)^2 (25) = 1350𝑥^2

Term 4: C(4,3)(3𝑥)^1 (-5)^3 = 4(3𝑥)(-125) = -1500𝑥

Term 5: C(4,4)(3𝑥)^0 (-5)^4 = 1(1)(625) = 625

Now, we can combine all the terms to obtain the expanded form:

81𝑥^4 - 540𝑥^3 + 1350𝑥^2 - 1500𝑥 + 625

So, the final answer obtained by expanding (3𝑥 − 5)^4 using Binomial Expansion is indeed:
81𝑥^4 - 540𝑥^3 + 1350𝑥^2 - 1500𝑥 + 625