91Ó°ÊÓ

Combining like terms is a fundamental skill in algebra. When we talk about like terms, we mean terms that have the same variables raised to the same powers. For example, in the expression a^{2}+3a^{2}-5a-6a+3-7, the terms with \(a^{2}\) and the terms with \(a\) are considered like terms. Like terms can be added or subtracted by combining their coefficients, which are the numbers in front of the variables.
For instance:

• oa^{2}+3a^{2}e= 4a^{2}
• oa^{-5a-6a= -11a}
• oa^{3 - 7 = -4}

It’s important to remember that only the coefficients are combined. The variables and their exponents remain unchanged.

Polynomial addition involves summing two or more polynomials by combining their corresponding terms. Here, each polynomial term must be aligned correctly by matching like terms. Look at the example given:a^{2} - 5a + 3 and3a^{2} - 6a - 7. To add these polynomials, we align and combine the like terms.
First, rewrite the expression as:
a^{2} - 5a + 3 + (3a^{2} - 6a - 7).
Then, group the like terms by their degrees:

• oa^{2} + 3a^{2}
• oa^{-5a - 6a}
• oa^{3 - 7}

Finally, add these groups to get the simplified polynomial:a^{4a^{2} - 11a - 4}.

Simplifying expressions is all about making complex mathematical expressions more concise. This includes combining like terms, adding or subtracting polynomials, and reducing the expression to its simplest form. Here’s how we simplified the given expression:
Initially, we had:a^{(a^{2} - 5a + 3) + (3a^{2} - 6a - 7)}.
We began by grouping like terms:a^{a^{2} + 3a^{2} - 5a - 6a + 3 - 7}.
Next, we combined the coefficients of the like terms:a^{(a^{2} + 3a^{2})} converted to a^{4a^{2}}.
a^{-5a - 6a} changed toa^{-11a}
a^{3 - 7} modified to a^{-4}.
Thus, the simplified form of the given polynomial expression is:a^{4a^{2} - 11a - 4}.
Simplifying expressions makes them easier to work with in future calculations.