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Factorise (x+y)^3- (x^3+y^3) plzzz answer ​

Sagot :

Answer:

[tex] \huge \boxed{ \boxed{ \tt 2xy(x + y)}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • factoring
  • PEMDAS

tips and formulas:

  • (a+b)³=a³+3a²b+3ab²+b³
  • a³+b³=(a+b)(a²-ab+b²)

let's solve:

  1. [tex] \sf \: use \: 2nd \: formula \: to \: simplify : \\ \sf(x + y {)}^{3} - (x + y)( {x}^{2} - xy + {y}^{2} )[/tex]
  2. [tex] \sf factor \: out \: (x + y) : \\ (x + y )\{(x + y)^{2} - ( {x}^{2} - xy + {y}^{2} \}[/tex]
  3. [tex] \sf simplify : \\ (x + y {)} \{ {x}^{2} + 2xy + {y}^{2} - {x}^{2} + xy - {y}^{2} \}[/tex]
  4. [tex] \sf collect \: and \: combine \: like \: terms : \\ (x + y) \{2xy \}[/tex]
  5. [tex] \sf \: rewrite : \\ 2xy(x + y)[/tex]

and

we are done

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