Question

Find the like term of $4{{z}^{4}}$.
A) $5{{z}^{3}}$
B) $5{{z}^{2}}$
C) $5{{z}^{4}}$
D) $5z$

Answer 1

Hint: Here we have to find the like term of $4{{z}^{4}}$. So coefficient can be changed but ${{z}^{4}}$ should be same. Check the options and you will get the answer.

Complete step by step solution: Like terms are the terms whose variables and exponents are the same.
The coefficients that are the number you multiply by can be different.
In the given value $4{{z}^{4}}$, $4$ is the coefficient hence it can be different. But the term ${{z}^{4}}$ should be the same.
In the first option, the coefficient is $5$, but the terms are not the same. Hence it is not alike term. Similarly, for option B and D coefficient is $5$ and terms are not same. So this is also not a like term.
Also, for option C, we can see that coefficient is $5$ and the terms are the same.
So the like term of $4{{z}^{4}}$ is $5{{z}^{4}}$.
Hence option C satisfies all the requirement of like terms.

A correct answer is an option (C).

Additional information:
Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily. To combine like terms, we add the coefficients and keep the variables the same. We can't combine unlike terms because that's like trying to add apples and oranges! Terms like ${{x}^{2}}yz$ and $x{{y}^{2}}z$ look a lot alike, but they aren't and cannot be combined. Write the terms carefully when working out problems.

Note: Basically, the difference between like term and unlike terms must be known. Also, sometimes jumbling occurs between the terms like ${{x}^{2}}yz$ and $x{{y}^{2}}z$. Terms obey the associative property of multiplication - that is, $xy$ and $yx$ are like terms, as is $x{{y}^{2}}$ and $y{{x}^{2}}$.