Question

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

Answer 1

Hint: In this question, we are having two terms on both the sides of the plus sign. We will simplify this equation in two steps. We will first expand both the terms individually. After that, we will combine the like terms by adding the expansion of both the terms.

Complete step by step answer:
We are given $3y\left( {y - 2} \right) + 4\left( {y - 2} \right)$.
Let us first consider the first term $3y\left( {y - 2} \right)$. We can expand it by multiplying $3y$to both the elements given in the bracket which are $y$and $2$ respectively, keeping the sign between them as it is.
$3y\left( {y - 2} \right) \Rightarrow 3{y^2} - 6y$
Now, we will do the same procedure for the second term $4\left( {y - 2} \right)$. We can expand it by multiplying $4$ to both the elements given in the bracket which are $y$ and $2$ respectively, keeping the sign between them as it is.
$4\left( {y - 2} \right) \Rightarrow 4y - 8$
Now, we will add both the terms
$
  3y\left( {y - 2} \right) + 4\left( {y - 2} \right) \\
   = 3{y^2} - 6y + 4y - 8 \\
 $
We have to combine like terms now. Like terms are the terms who have the same variable with the same power.
Here, we can see that the terms $ - 6y$ and $ + 4y$ has the same variable with the same power which is $y$.
Therefore, we can combine both these terms as :
$
  3y\left( {y - 2} \right) + 4\left( {y - 2} \right) \\
   = 3{y^2} - 6y + 4y - 8 \\
   = 3{y^2} + ( - 6 + 4)y - 8 \\
   = 3{y^2} - 2y - 8 \\
 $

Thus, by simplifying $3y\left( {y - 2} \right) + 4\left( {y - 2} \right)$, we get the quadratic polynomial $3{y^2} - 2y - 8$ as our final answer.

Note: Here, we have used the concept of expanding the terms. There is an important thing to keep in mind while doing the expansion. We need to apply the distributive property to remove any parentheses or brackets and combine the like terms. The distributive property states that, \[a\left( {b + c} \right) = ab + ac\] and \[a\left( {b - c} \right) = ab - ac\].