How do you expand (x−y)3?

rheisf

rheisf

Answered

2021-12-27

How do you expand (xy)3?

Answer & Explanation

chumants6g

chumants6g

Expert

2021-12-28Added 33 answers

Explanation:
(xy)(xy)=x2xyxy+y2
=x22xy+y2
=(x22xy+y2)(xy)
x3x2y2x2y+2xy2+xy2y3
=x33x2y+3xy2y3
nghodlokl

nghodlokl

Expert

2021-12-29Added 33 answers

Explanation:
(xy)3=(xy)(xy)(xy)
Expand the first two brackets:
(xy)(xy)=x2xyxy+y2
x2+y22xy
Multiply the result by the last two brackets:
(x2+y22xy)(xy)=x3x2y+xy2y32x2y+2xy2
x3y33x2y+3xy2
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

Vasquez

Expert

2022-01-08Added 457 answers

Explanation

The expression (xy)3 can be written as, (xy)(xy)(xy)
First simplify (x-y)(x-y)by binomial multiplication.
(xy)(xy)=x22xy+y2
Now multiply (x-y) with x22xy+y2
(xy)(xy)(xy)=(xy)(x22xy+y2)
=x32x2y+xy2yx2+2xy2y3
=x33x2y+3xy2y3
Thus, the expansion of (xy)3 is x3y33x2y+3xy2

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