Question

Add. $$ (4 a 5+5 a 3-a)+(3 a 4-2 a 2+7) $$

   Add.
$$
(4 a 5+5 a 3-a)+(3 a 4-2 a 2+7)
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 5, Problem 14

Instant Answer

Solved by Expert Emily Himsel

01/27/2022

Step 1

Like terms are terms that have the same variable and exponent. In this case, the like terms are $4a^5$ and $-a$, $5a^3$ and $3a^4$, and $-2a^2$ and $7$. Show more…

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Add. $$ (4 a 5+5 a 3-a)+(3 a 4-2 a 2+7) $$

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Key Concepts

Standard Form of a Polynomial

Writing a polynomial in standard form means arranging its terms in descending order based on the power of the variable. This format not only makes the polynomial easier to read and compare but is also beneficial when performing operations such as addition, subtraction, and even solving polynomial equations.

Polynomial Addition

Polynomial addition is the process of combining two or more polynomials by adding their corresponding coefficients of like-degree terms. This operation relies on the commutative and associative properties of addition to rearrange and group terms with the same variable exponent, making it a fundamental concept for manipulating algebraic expressions.

Combining Like Terms

Combining like terms involves adding or subtracting coefficients of terms that have identical variable parts, such as the same base raised to the same power. This technique simplifies polynomial expressions, reducing them to a form where each term represents a unique degree, which is essential for further algebraic manipulation.

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