Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Multiplication
Polynomial multiplication involves distributing each term of one polynomial to every term of another polynomial. In this case, we multiply the binomial (x + 1) by the trinomial (x^2 - x + 1), ensuring that each term in the first polynomial is multiplied by each term in the second. This process results in a new polynomial that combines like terms.
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Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing us to distribute a single term across a sum or difference. This property is essential in polynomial multiplication, as it helps simplify the process of multiplying polynomials by ensuring that each term is accounted for in the final expression.
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Combining Like Terms
Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. After multiplying the polynomials, we will often have several terms that can be combined to create a more concise polynomial expression, making it easier to interpret and work with.
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