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

1 Answer
Jun 22, 2018

Answer:

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.