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a. \( (3 x+7)(x+3) \)

Ask by Goodwin Montgomery. in the United States
Mar 15,2025

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\( (3x + 7)(x + 3) = 3x^2 + 16x + 21 \)

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Beyond the Answer

To understand how to expand \( (3x + 7)(x + 3) \), let’s use the distributive property (also called the FOIL method for binomials). Start by multiplying each term in the first set of parentheses by each term in the second: \( 3x \times x + 3x \times 3 + 7 \times x + 7 \times 3 \). This evaluates to \( 3x^2 + 9x + 7x + 21 \). Combine like terms to get the final result: \( 3x^2 + 16x + 21 \). In real-world situations, such polynomial expansions can reflect calculations involving area, like figuring out the total area of rectangular regions where dimensions are expressed in terms of variables. This method can apply to fields as varied as geometry, economics, and physics! For example, if you’re designing a garden, using variables to represent dimensions could make planning and predicting growth based on different arrangements much simpler.

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