Question

How do you use the binomial theorem to expand and simplify the expression `(y-4)^3`?

Answer 1

We can expand this expression by remembering the rule for expanding cubic functions.

Explanation:

You could rewrite `(y-4)^3` as `(y-4)(y-4)(y-4)` or as `(y-4)(y^2-8y+16)`, but that would take ages to solve! Instead, let's think of it this way:

`(a-b)^3=a^3-3a^2b+3ab^2-b^3`

Using this, we can make our equation look a lot less scary:

`(y-4)^3=y^3-3(y^2)(4)+3(y)(4^2)-(4^3)`
`(y-4)^3=y^3-12y^2+48y-64`

Since no like terms exist, our equation is completely simplified.