MHB Partial Fraction Simplification

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To simplify the partial fraction expression, the multiplication of the binomials (Bx + C)(x + 3) needs to be performed. This results in Bx^2 + (3B + C)x + 3C. When combined with the other term (x^2 + 9), the overall expression becomes (B + 1)x^2 + (3B + C)x + (9 + 3C). This matches the textbook's formulation, confirming the derivation process. Understanding this multiplication is crucial for mastering partial fraction decomposition.
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I have this partial fraction:

$$ 18 = (x^2 + 9) + (Bx + C)(x + 3)$$

which the textbook says is equal to:

$$(B + 1)x^2 + (C + 3B)x + (9 + 3C)$$

But I don't follow this step. How do I derive this?
 
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Okay, we begin with:

$$\left(x^2+9\right)+(Bx+C)(x+3)$$

What to you get when you carry out the indicated multiplication of the two binomial expressions?
 

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