Find solutions to your questions with the help of IDNLearn.com's expert community. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
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]
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]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.