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

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

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Answer 1 · 2017-01-11T10:49:23

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

Explanation:

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

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

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

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

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

= $y \times y - 3 \times y - 3 \times y - 3 \times (- 3)$ $yxxy-3xxy-3xxy-3xx(-3)$

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

= $y^{2} - 6 y + 9$ $y^2-6y+9$

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

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

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

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

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

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

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

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

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Explanation:

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

1 Answer

Explanation:

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