Here are the essential concepts you must grasp in order to answer the question correctly.
Binomials
A binomial is a polynomial that consists of exactly two terms, which can be separated by a plus or minus sign. In the expression (7x³ + 5)(x² - 2), both (7x³ + 5) and (x² - 2) are binomials. Understanding how to manipulate binomials is essential for performing operations like addition, subtraction, and multiplication.
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FOIL Method
The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms of the binomials. For example, in (7x³ + 5)(x² - 2), you would multiply the First terms (7x³ and x²), the Outside terms (7x³ and -2), the Inside terms (5 and x²), and the Last terms (5 and -2) to find the product.
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Combining Like Terms
After applying the FOIL method, the resulting expression may contain like terms, which are terms that have the same variable raised to the same power. Combining like terms involves adding or subtracting these terms to simplify the expression. This step is crucial for arriving at the final, simplified form of the product of the binomials.
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