How do you write the expression $(y-3)(y-3)(y-3)$ using exponents?

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Answer 1 · 2017-01-11T10:49:23

$(y-3)(y-3)(y-3)=(y-3)^3=y^3-9y^2+27y-27$

This is a product of three binomials, who are all the same i.e. $(y-3)(y-3)(y-3)$ .

We can write it simply as $(y-3)^3$ .

For actual mutiplication, we use distributive property, first over $(y-3)(y-3)$ and then multiplying the result by $(y-3)$

$(y-3)(y-3)$

= $y(y-3)-3(y-3)$

= $yxxy-3xxy-3xxy-3xx(-3)$

= $y^2-3y-3y+9$

= $y^2-6y+9$

and now multiplying above again by $(y-3)$

$(y-3)(y-3)(y-3)$

= $(y-3)(y^2-6y+9)$

= $y(y^2-6y+9)-3(y^2-6y+9)$

= $yxxy^2-6yxxy+9xxy-3xxy^2-3xx(-6y)-3xx9$

= $y^3-6y^2+9y-3y^2+18y-27$

= $y^3-9y^2+27y-27$

How do you write the expression (y-3)(y-3)(y-3)(y-3)(y-3)(y-3) using exponents?