rheisf

Answered

2021-12-27

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

Answer & Explanation

chumants6g

Expert

2021-12-28Added 33 answers

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

Expert

2021-12-29Added 33 answers

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

Expert

2022-01-08Added 457 answers

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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