Question

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

Answer 1

`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}`