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

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Answer 1 · 2018-06-22T13:03:46

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

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.

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