Question 56 (b)

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

$x^{4} + 3 x^{3} y + 3 x^{2} y^{2} - 3 x^{3} y - 3 x y^{2} + y^{4} - 3 x^{2} y^{2}$

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Solution

$x^{4} + 3 x^{3} y + 3 x^{2} y^{2} - 3 x^{3} y - 3 x y^{3} + y^{4} - 3 x^{2} y^{2}$
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 trinomial.

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