Problem

Find the product of the functions \(f(x) = 3x + 2\) and \(g(x) = 2x - 5\)

Answer

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Answer

Combining like terms, we get \(h(x) = 6x^2 - 11x - 10\).

Steps

Step 1 ：The product of two functions \(f(x)\) and \(g(x)\) is given by \(h(x) = f(x) \cdot g(x)\).

Step 2 ：Substitute \(f(x) = 3x + 2\) and \(g(x) = 2x - 5\) into the above formula, we get \(h(x) = (3x + 2) \cdot (2x - 5)\).

Step 3 ：Using the distributive property of multiplication over addition, we expand the above expression: \(h(x) = 3x \cdot 2x - 3x \cdot 5 + 2 \cdot 2x - 2 \cdot 5\).

Step 4 ：This simplifies to \(h(x) = 6x^2 - 15x + 4x - 10\).

Step 5 ：Combining like terms, we get \(h(x) = 6x^2 - 11x - 10\).

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