Question

How do you simplify $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}$?

Answer 1

Hint: We have to find the like terms in $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}$ and then simplify them. We check the algebraic terms in the equation of $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}$ and also the power values. Terms with the same degree and same algebraic forms will be combined as like terms.

Complete step-by-step solution:
In the equation of $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}$, the variable terms are $x,y$.
There are two types of power or indices values for variables $x,y$.
The terms joined by addition are $2{{x}^{2}}{{y}^{3}}$ and $4{{x}^{2}}{{y}^{3}}$ are like terms as they have same variable and the indices value is also same which is 5.
We now simplify the like terms using the binary operation between them.
The simplification happens for the coefficients of the terms.
We add 2 and 4 to get \[2+4=6\].
The combined solution will be $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}=6{{x}^{2}}{{y}^{3}}$
This way we simplify $2{{x}^{2}}{{y}^{3}}+4{{x}^{2}}{{y}^{3}}$ and get $6{{x}^{2}}{{y}^{3}}$.

Note: In the calculation we must be careful about the number of variables available in the terms. Unlike terms can be created with different variables but same indices value. In compound terms we check the individual indices.