Simplify the expression $\left( {3{y^2} + 5y - 4} \right) - \left( {8y - {y^2} - 4} \right)$

Hint: The problem is given in the form of algebraic expression. An algebraic expression is an expression which is made up of variables and constants. Here, we are given two algebraic expressions and we need to subtract them. First, we will change the signs of the expression which we need to subtract. After changing the signs we will place the like terms together to make the calculation easier. Like terms are the terms that have the same variables and powers and unlike terms are those terms whose variables and powers are different from each other. The coefficients do not need to match. For example, $41y$ and $29y$ are like terms whereas $41x$ and $29y$ are unlike terms because their variables are different.

Complete step-by-step solution:
Given: $\left( {3{y^2} + 5y - 4} \right) - \left( {8y - {y^2} - 4} \right)$
On opening the bracket, we get
$ \Rightarrow 3{y^2} + 5y - 4 - 8y + {y^2} + 4$
Now we re-rearrange the like terms which give us
$ \Rightarrow 3{y^2} + {y^2} + 5y - 8y + 4 - 4$
On addition and subtraction of like terms, we get
$ \Rightarrow 4{y^2} - 3y$
Pull out like factors
$ \Rightarrow y\left( {4y - 3} \right)$
Therefore, on simplifying $\left( {3{y^2} + 5y - 4} \right) - \left( {8y - {y^2} - 4} \right)$, we get $y\left( {4y - 3} \right)$.

Note: Here, we have changed the signs (positive sign to negative sign and vice versa) of an algebraic expression which we had to subtract from another algebraic expression because here we are subtracting two algebraic expressions. Don’t repeat this step in addition to algebraic expressions. Arrange the like terms together to make the calculations easier. Students must be aware of the like and unlike terms when you are adding or subtracting algebraic expressions. You can only perform the addition or subtraction on the like terms. Take care of the signs while subtracting or adding the expressions. Check the calculations.