Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Multiplication
Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process, often referred to as the FOIL method for binomials, ensures that all combinations of terms are accounted for. For example, in the expression (3x + 5)(2x - 9), you would multiply 3x by 2x, 3x by -9, 5 by 2x, and 5 by -9, combining like terms afterward.
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Combining Like Terms
Combining like terms is a fundamental algebraic process that simplifies expressions by merging terms that have the same variable raised to the same power. For instance, in the expression 6x^2 + 3x - 2x^2 + 4, the like terms 6x^2 and -2x^2 can be combined to yield 4x^2. This step is crucial for simplifying the result of polynomial operations.
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Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing for the multiplication of a single term by a sum or difference. This property is essential when expanding expressions, such as when subtracting one polynomial from another. In the given problem, applying the distributive property helps to correctly handle the subtraction of the second polynomial from the first, ensuring accurate results.
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