rheisf

2021-12-27

How do you expand ${\left(x-y\right)}^{3}$?

### Answer & Explanation

chumants6g

Explanation:
$\left(x-y\right)\left(x-y\right)={x}^{2}-xy-xy+{y}^{2}$
$={x}^{2}-2xy+{y}^{2}$
$=\left({x}^{2}-2xy+{y}^{2}\right)\left(x-y\right)$
${x}^{3}-{x}^{2}y-2{x}^{2}y+2x{y}^{2}+x{y}^{2}-{y}^{3}$
$={x}^{3}-3{x}^{2}y+3x{y}^{2}-{y}^{3}$

nghodlokl

Explanation:
${\left(x-y\right)}^{3}=\left(x-y\right)\left(x-y\right)\left(x-y\right)$
Expand the first two brackets:
$\left(x-y\right)\left(x-y\right)={x}^{2}-xy-xy+{y}^{2}$
$⇒{x}^{2}+{y}^{2}-2xy$
Multiply the result by the last two brackets:
$\left({x}^{2}+{y}^{2}-2xy\right)\left(x-y\right)={x}^{3}-{x}^{2}y+x{y}^{2}-{y}^{3}-2{x}^{2}y+2x{y}^{2}$
$⇒{x}^{3}-{y}^{3}-3{x}^{2}y+3x{y}^{2}$
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

Explanation

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

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