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c. \( (3 c+a)(4 c-5 a) \)

Ask by Barker Wood. in the United States
Mar 15,2025

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\( (3c+a)(4c-5a) = 12c^{2}-11ca-5a^{2} \)

Solución

Calculate or simplify the expression \( (3c+a)(4c-5a) \). Simplify the expression by following steps: - step0: Solution: \(\left(3c+a\right)\left(4c-5a\right)\) - step1: Apply the distributive property: \(3c\times 4c-3c\times 5a+a\times 4c-a\times 5a\) - step2: Multiply the terms: \(12c^{2}-15ca+4ac-5a^{2}\) - step3: Add the terms: \(12c^{2}-11ca-5a^{2}\) The expression \( (3c+a)(4c-5a) \) simplifies to \( 12c^{2}-11ca-5a^{2} \).

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Beyond the Answer

Did you know that the expression \( (3c + a)(4c - 5a) \) can be expanded using the distributive property, also known as the FOIL method for binomials? By multiplying the first terms, outer terms, inner terms, and last terms together, you combine like terms to simplify the expression into a more manageable format: \( 12c^2 - 15ac + 4ac - 5a^2 \), which ultimately results in \( 12c^2 - 11ac - 5a^2 \). How neat is that? Now, in real-world applications, expressions like this show up when calculating areas or volumes, particularly in engineering or architecture! For instance, if \( 3c + a \) represented the dimensions of one side of a rectangle and \( 4c - 5a \) represented the other, you'd be calculating the total area. It’s a vital skill used in designing structures, allowing architects to ensure their designs are both innovative and practical.

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