To multiply the expression \((5x + 2)(x^2 - 3x + 6)\), we can use the distributive property (sometimes referred to as the FOIL method for binomials, although here one factor is a trinomial).
We'll distribute each term in the first parentheses by each term in the second parentheses:
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Multiply \(5x\) by each term in \(x^2 - 3x + 6\):
- \(5x \cdot x^2 = 5x^3\)
- \(5x \cdot (-3x) = -15x^2\)
- \(5x \cdot 6 = 30x\)
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Multiply \(2\) by each term in \(x^2 - 3x + 6\):
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-3x) = -6x\)
- \(2 \cdot 6 = 12\)
Now, we can combine all these products together:
\[ 5x^3 - 15x^2 + 30x + 2x^2 - 6x + 12 \]
Next, combine like terms:
- For \(x^2\) terms: \(-15x^2 + 2x^2 = -13x^2\)
- For \(x\) terms: \(30x - 6x = 24x\)
So, combining everything, we get:
\[ 5x^3 - 13x^2 + 24x + 12 \]
Thus, the final result of the multiplication \((5x + 2)(x^2 - 3x + 6)\) is:
\[ \boxed{5x^3 - 13x^2 + 24x + 12} \]