Question

How do you simplify the expression $(4x - 3y)(x + 5y)$?

Answer 1

Hint: According to the question given in the question we have to simplify the expression $(4x - 3y)(x + 5y)$. So, first of all to determine the simplification or we can say that to determine the values of the variables x and y which are mentioned in the question we have to multiply the terms of the expression.
Now, we have to arrange the terms which are obtained after the multiplication for that we have to take all the same variables on the same side and other variables to the other side.
Now, we have to add and subtract the terms and variables which are x and y as mentioned in the expression obtained which can be added and subtracted.

Complete step-by-step solution:
Step 1: First of all to determine the simplification or we can say that to determine the values of the variables x and y which are mentioned in the question we have to multiply the terms of the expression. Hence, on multiplying all the terms,
 $
   \Rightarrow 4x(x + 5y) - 3y(x + 5y) = 0 \\
   \Rightarrow 4{x^2} + 20xy - 3xy - 15{y^2} = 0
 $
Step 2: Now, we have to arrange the terms which are obtained after the multiplication for that we have to take all the same variables on the same side and other variables to the other side. Hence,
$ \Rightarrow 4{x^2} - 15{y^2} = - 20xy + 3xy$
Step 3: Now, we have to add and subtract the terms and variables which are x and y as mentioned in the expression obtained which can be added and subtracted.
$ \Rightarrow 4{x^2} - 15{y^2} + 17xy = 0$

Hence, we have simplified the expression $(4x - 3y)(x + 5y)$ which is $4{x^2} - 15{y^2} + 17xy = 0$.

Note: It is necessary that we have to multiply all the terms of the one expression in which there are two variables x and y so we have to multiply these variables to each-other.
It is necessary that we have to arrange the terms which are obtained after the multiplication for that we have to take all the same variables on the same side and other variables to the other side.