# Math Help - [SOLVED] Expanding Cubic Brackets

1. ## [SOLVED] Expanding Cubic Brackets

I'm stuck on a particular maths question which asks;

Write $(1 + \sqrt{5})^3$ in the form $a + b\sqrt{5}$, where a and b are integers.

I do have a worked solution to this problem, but it isn't much help, as I'm uncertain as to how to expand cubic brackets.

Could someone please explain how to expand backets of the form $(a + b)^3$ and $(a - b)^3$?

2. Originally Posted by Flay
I'm stuck on a particular maths question which asks;

Write $(1 + \sqrt{5})^3$ in the form $a + b\sqrt{5}$, where a and b are integers.

I do have a worked solution to this problem, but it isn't much help, as I'm uncertain as to how to expand cubic brackets.

Could someone please explain how to expand backets of the form $(a + b)^3$ and $(a - b)^3$?
You should know the binomial expansion with coefficients given by Pascal's triangle if not the general form.

Use the binomial expansion:

$(a+b)^3=a^3+3a^2b+3ab^2+b^3$

with $a=1$, and $b=\sqrt{5}$ , then:

$(1+\sqrt{5})^3=1+3\sqrt{5}+3\times 5+5 \sqrt{5}$

RonL

3. Thanks very much.