Question
Simplify the combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial:
$x^4+3 x^3 y+3 x^2 y^2-3 x^3 y-3 x y^3+y^4-3 x^2 y^2$
$x^4+3 x^3 y+3 x^2 y^2-3 x^3 y-3 x y^3+y^4-3 x^2 y^2$
✓
Answer
We have
$x^4+3 x^3 y+3 x^2 y^2-3 x^3 y-3 x y^3+y^4-3 x^2 y^2$
By combining the like terms
$=x^4+3 x^3 y-3 x^3 y+3 x^2 y^2-3 x^2 y^2-3 x^3 y+y^4$
$=x^4+0+0-3 x^3 y+y^4=x^4+y^4-3 x^3 y$
The expression contains three terms so, it is binomial.
$x^4+3 x^3 y+3 x^2 y^2-3 x^3 y-3 x y^3+y^4-3 x^2 y^2$
By combining the like terms
$=x^4+3 x^3 y-3 x^3 y+3 x^2 y^2-3 x^2 y^2-3 x^3 y+y^4$
$=x^4+0+0-3 x^3 y+y^4=x^4+y^4-3 x^3 y$
The expression contains three terms so, it is binomial.
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