Solved: "How do you expand (x−y)3?"

High School
Algebra
Algebra I
Quadratic function and equation

rheisf

Answered question

2021-12-27

How do you expand

{(x - y)}^{3}

Answer & Explanation

chumants6g

Beginner2021-12-28Added 33 answers

Explanation:

(x - y) (x - y) = x^{2} - x y - x y + y^{2}

= x^{2} - 2 x y + y^{2}

= (x^{2} - 2 x y + y^{2}) (x - y)

x^{3} - x^{2} y - 2 x^{2} y + 2 x y^{2} + x y^{2} - y^{3}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}

nghodlokl

Beginner2021-12-29Added 33 answers

Explanation:

{(x - y)}^{3} = (x - y) (x - y) (x - y)

Expand the first two brackets:

(x - y) (x - y) = x^{2} - x y - x y + y^{2}

\Rightarrow x^{2} + y^{2} - 2 x y

Multiply the result by the last two brackets:

(x^{2} + y^{2} - 2 x y) (x - y) = x^{3} - x^{2} y + x y^{2} - y^{3} - 2 x^{2} y + 2 x y^{2}

\Rightarrow x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}

Always expand each term in the bracket by all the other terms in the other brackets, but never multiply two or more terms in the same bracket.

Vasquez

Expert2022-01-08Added 669 answers

Explanation

The expression $(x - y)^{3}$ can be written as, $(x - y) (x - y) (x - y)$
First simplify (x-y)(x-y)by binomial multiplication.
$(x - y) (x - y) = x^{2} - 2 x y + y^{2}$
Now multiply (x-y) with $x^{2} - 2 x y + y^{2}$
$(x - y) (x - y) (x - y) = (x - y) (x^{2} - 2 x y + y^{2})$
$= x^{3} - 2 x^{2} y + x y^{2} - y x^{2} + 2 x y^{2} - y^{3}$
$= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$
Thus, the expansion of $(x - y)^{3} i s x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}$

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