Question

Simplify the given algebraic expression: \[\left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right)\]

Answer 1

Hint: Here we need to simplify the given algebraic expression. For that, we will first rearrange the terms inside the parentheses. Then we will remove the parentheses and after removing the parentheses, we will combine the like terms i.e. we will add or subtract the like terms. Then after combining the like terms, we will rearrange the terms to get the final answer.

Complete step-by-step answer:
Here we need to find the simplified value of the given algebraic expression i.e. \[\left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right)\]
We will first rearrange the terms inside the parentheses.
\[ \Rightarrow \left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right) = \left( {5{p^2} - 3} \right) + \left( { - 3{p^3} + 2{p^2}} \right)\]
Now, we will remove the parentheses and rewrite the expression.
\[ \Rightarrow \left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right) = 5{p^2} - 3 - 3{p^3} + 2{p^2}\]
Now, we will combine the like terms i.e. we will add or subtract the like terms.
On adding or subtracting the like terms, we get
\[ \Rightarrow \left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right) = 7{p^2} - 3 - 3{p^3}\]
Now, we will again rearrange the terms.
\[ \Rightarrow \left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right) = - 3{p^3} + 7{p^2} - 3\]
Hence, the simplified value of the given algebraic expression i.e. \[\left( {5{p^2} - 3} \right) + \left( {2{p^2} - 3{p^3}} \right)\] is equal to \[ - 3{p^3} + 7{p^2} - 3\].
Therefore, the required answer of this problem is \[ - 3{p^3} + 7{p^2} - 3\].

Note: Here we have simplified the given algebraic expression by first removing the parentheses and then combining the like terms. Here like terms are defined as the terms which contain the same variable which is raised to the same power. So combining the like terms means to add or subtract the coefficients keeping the variable same. In mathematics, an algebraic expression is defined as an expression which is formed by the combination of constants and variables using algebraic operations like addition, subtraction and multiplication. To simplify the expression, we need to remove the parentheses first and then we can simplify it further.