Find the number of terms in the expression obtained after adding the expressions
$4 x^{2} - 2 y z + 3 x^{3}$ and $2 z y + x^{2} + y^{3}$

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Solution

$(4 x^{2} - 2 y z + 3 x^{3}) + (2 z y + x^{2} + y^{3})$
$= 9 x^{2} - 2 y z + 3 x^{3} + 2 z y + x^{2} + y^{3}$
Grouping the like terms together,
we get
$= (9 x^{2} + x^{2}) + (- 2 + 2) y z + 3 x^{3} + y^{3}$
$= x^{2} (9 + 1) + 0 y z + 3 x^{3} + y^{3}$
$= 10 x^{2} + 3 x^{3} + y^{3}$

Number of terms = 3

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