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Use the binomial expansion
(a+b)⁴ = a⁴+4a³b+6a²b²+4ab³+b⁴ to expand and simplify (x-3)⁴​

1 Answer

3 votes

Answer:


x^4-12x^3+54x^2-108x+81

Explanation:

We have been given the following binomial expansion for (a + b)⁴:


\boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4}

To use this to expand and simplify (x - 3)⁴, first identity the values of a and b:

  • a = x
  • b = -3

Substitute the values of a and b into the expansion, and simplify:


\begin{aligned}(x-3)^4&=x^4+4x^3(-3)+6x^2(-3)^2+4x(-3)^3+(-3)^4\\\\&=x^4+4x^3(-3)+6x^2(9)+4x(-27)+81\\\\&=x^4-12x^3+54x^2-108x+81\end{aligned}

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