Add or subtract the polynomials, gather like terms, and write the simplified expression in stand

step 1 The first thing we're being asked to do is to subtract the two given polynomials. Well, the firs

Add or subtract the polynomials, gather like terms, and...

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Key Concepts

Polynomials

Polynomials are algebraic expressions made up of terms that include variables raised to nonnegative integer powers and coefficients. They provide a fundamental way to represent functions and relationships in algebra, and operations on them include addition, subtraction, and multiplication among others.

Addition and Subtraction of Polynomials

Adding or subtracting polynomials involves combining corresponding terms from each polynomial. This operation requires distributing any negative signs across the polynomial being subtracted and then merging terms that have the same variable raised to the same power.

Like Terms

Like terms in a polynomial are terms that have the exact same variable part (i.e., the same variable and exponent). Combining like terms is essential in simplifying polynomial expressions because it consolidates similar components into a single term, thereby reducing the expression to a simpler form.

Standard Form

Writing a polynomial in standard form involves arranging its terms in descending order based on the degree of the term. This ordering makes it easier to read the polynomial and identify properties such as its degree and leading coefficient.

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