How do you simplify $\left( {4{x^2}y - 3x{y^2}} \right) - \left( {3{x^2}y - 8x{y^2}} \right)$ ?

Hint: We have been given an algebraic expression having four terms which are grouped into two brackets. An algebraic expression is a collection of terms with variables and constants which are joined together through algebraic operators. We have to simplify the expression. Simplifying this expression means adding or subtracting similar terms such that we are left with only unique terms in the expression. The similar terms here means the same variable having the same degree.

Complete step by step solution:
We have been given to simplify the algebraic expression $\left( {4{x^2}y - 3x{y^2}} \right) - \left( {3{x^2}y - 8x{y^2}} \right)$.
This expression has four terms. When we are simplifying an algebraic expression we have to group together the similar terms. The algebraic operators can be simplified only for similar terms. Similar terms are those terms in which the degree of the variables are the same.
In the given expression we first try to remove the brackets.
$\left( {4{x^2}y - 3x{y^2}} \right) - \left( {3{x^2}y - 8x{y^2}} \right) = 4{x^2}y - 3x{y^2} - 3{x^2}y + 8x{y^2}$
Now we can see that the first term and third term are similar as both have the same degree of the variables, i.e. ${x^2}y$. So these will be grouped together.
Similarly, we can group the second and fourth terms as both have the same degree of variables, i.e. $x{y^2}$.
Thus,
 \[4{x^2}y - 3x{y^2} - 3{x^2}y + 8x{y^2} = \left( {4{x^2}y - 3{x^2}y} \right) - \left( {3x{y^2} - 8x{y^2}} \right)\]
Now the arithmetic operation is carried on the coefficients in each group separately as follows,
 \[\left( {4{x^2}y - 3{x^2}y} \right) - \left( {3x{y^2} - 8x{y^2}} \right) = \left( {{x^2}y} \right) - \left( { - 5x{y^2}} \right) = {x^2}y + 5x{y^2}\]
This is the simplified form of the given expression.
So, the correct answer is “\[\left( {{x^2}y} \right) - \left( { - 5x{y^2}} \right) = {x^2}y + 5x{y^2}\] ”.

Note: When we have to simplify an algebraic expression containing different degrees of variables, we group together the similar terms and carry out the arithmetic operations on them. Dissimilar terms cannot be added or subtracted. Simplified form of an expression means where there are no similar terms left.