Question

Simplify (-6x + 5)3

Answer 1

To simplify the expression \((-6x + 5)^3\), we can use the binomial expansion formula, which states that:

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

In this case, let \(a = -6x\), \(b = 5\), and \(n = 3\). The binomial expansion becomes:

\[
(-6x + 5)^3 = \sum_{k=0}^{3} \binom{3}{k} (-6x)^{3-k} (5)^k
\]

Now we can calculate each term of the expansion:

- For \(k = 0\):
\[
\binom{3}{0} (-6x)^3 (5)^0 = 1 \cdot (-216x^3) \cdot 1 = -216x^3
\]

- For \(k = 1\):
\[
\binom{3}{1} (-6x)^2 (5)^1 = 3 \cdot 36x^2 \cdot 5 = 540x^2
\]

- For \(k = 2\):
\[
\binom{3}{2} (-6x)^1 (5)^2 = 3 \cdot (-6x) \cdot 25 = -450x
\]

- For \(k = 3\):
\[
\binom{3}{3} (-6x)^0 (5)^3 = 1 \cdot 1 \cdot 125 = 125
\]

Now, we can combine all these terms together:

\[
(-6x + 5)^3 = -216x^3 + 540x^2 - 450x + 125
\]

Thus, the simplified form of \((-6x + 5)^3\) is:

\[
\boxed{-216x^3 + 540x^2 - 450x + 125}
\]