The answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
To find the resultant expression, we need to apply the distributive property.
It can be defined by the following way:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
Also, we need to remember how to add like terms: The like terms are the terms that share the same variable and exponent, for example:
[tex]x+x+x^{2}=2x+x^{2}[/tex]
We were able to add only the two first terms since they were like terms (they share the same variable and the same exponent)
So , we are given the expression:
[tex](x+y)(x^{2}-xy+y^{2})[/tex]
Then, applying the distributive property, we have:
[tex](x+y)(x^{2}-xy+y^{2})=x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}\\\\x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}=x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}\\\\x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}=x^{3}+y^{3}[/tex]
Hence, the answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
Have a nice day!
