Sure! Let's multiply the given expressions step-by-step:
We need to multiply the two expressions: [tex]\((8x + 9)(x^2 + 3x - 1)\)[/tex].
Let's distribute each term in [tex]\((8x + 9)\)[/tex] through [tex]\((x^2 + 3x - 1)\)[/tex]. We'll start by multiplying [tex]\(8x\)[/tex] by each term in [tex]\((x^2 + 3x - 1)\)[/tex] and then do the same with [tex]\(9\)[/tex].
### Step 1: Distribute [tex]\(8x\)[/tex] to each term in [tex]\(x^2 + 3x - 1\)[/tex]
[tex]\[ 8x \cdot x^2 = 8x^3 \][/tex]
[tex]\[ 8x \cdot 3x = 24x^2 \][/tex]
[tex]\[ 8x \cdot (-1) = -8x \][/tex]
So, the terms we get from distributing [tex]\(8x\)[/tex] are: [tex]\(8x^3 + 24x^2 - 8x\)[/tex].
### Step 2: Distribute [tex]\(9\)[/tex] to each term in [tex]\(x^2 + 3x - 1\)[/tex]
[tex]\[ 9 \cdot x^2 = 9x^2 \][/tex]
[tex]\[ 9 \cdot 3x = 27x \][/tex]
[tex]\[ 9 \cdot (-1) = -9 \][/tex]
So, the terms we get from distributing [tex]\(9\)[/tex] are: [tex]\(9x^2 + 27x - 9\)[/tex].
### Step 3: Combine all the terms
Now we need to add all the like terms together:
[tex]\[ 8x^3 + 24x^2 - 8x + 9x^2 + 27x - 9 \][/tex]
### Step 4: Simplify by combining like terms
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 24x^2 + 9x^2 = 33x^2 \][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -8x + 27x = 19x \][/tex]
Finally, we gather all the terms together:
[tex]\[ 8x^3 + 33x^2 + 19x - 9 \][/tex]
So, the product of [tex]\((8x + 9)(x^2 + 3x - 1)\)[/tex] is:
[tex]\[ 8x^3 + 33x^2 + 19x - 9 \][/tex]
