rheisf

2021-12-27

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

chumants6g

Beginner2021-12-28Added 33 answers

Explanation:

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

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

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

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

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

nghodlokl

Beginner2021-12-29Added 33 answers

Explanation:

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

Expand the first two brackets:

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

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

Multiply the result by the last two brackets:

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

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

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.

Expand the first two brackets:

Multiply the result by the last two brackets:

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

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