Question

How do you simplify \[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\]?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will first understand how we can do additions or subtractions with different types of variables. After that, we will add the terms of square of y. After that, we will add the terms of y. After that, we will add the constants. After that, we will get our answer.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to simplify the term \[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\]. Or, we can say we have to solve and find the simplified value of the term \[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\].
Before solving this question, let us first understand how we add the variables.
We can only add the terms when there are the same variables with the same powers. We can see from the following examples:
\[2{{y}^{2}}+{{y}^{2}}+y=2{{y}^{2}}+1\times {{y}^{2}}+1\times y=3{{y}^{2}}+y\]
\[4{{y}^{2}}-2{{y}^{2}}+9y=2{{y}^{2}}+9y\]
Now, we can simplify the given term.
The given term is
\[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\]
Let us first arrange the terms.
\[\Rightarrow 5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10=5{{y}^{2}}-6{{y}^{2}}+y+8y-10-6\]
Let us first add the terms of \[{{y}^{2}}\], we can write the above equation as
\[\Rightarrow 5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10=-1\times {{y}^{2}}+y+8y-10-6\]
The above equation can also be written as
\[\Rightarrow 5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10=-{{y}^{2}}+y+8y-10-6\]
Now, adding the terms of ‘y’, we can write the above equation as
\[\Rightarrow 5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10=-{{y}^{2}}+9y-10-6\]
Now, adding the constant terms, we can write the above equation as
\[\Rightarrow 5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10=-{{y}^{2}}+9y-16\]

Now, we have simplified the term \[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\]. The simplified value of the term \[5{{y}^{2}}+y-6-6{{y}^{2}}+8y-10\] is \[-{{y}^{2}}+9y-16\].

Note: As we can see that this question is from the topic of algebra, so we should have a better knowledge in that topic. For solving this type of question, we should know that we can only add the terms whose coefficients or variables are the same with the same powers. Always remember that if no constant term is multiplied with the variable term, then the term is always already multiplied with 1. For example, we can see the following:
\[{{y}^{2}}=1\times {{y}^{2}}\]
\[y=1\times y\]