Answer :
Sure! Let's work through the problem step by step.
We want to multiply and simplify the expression [tex]\((3x + 5)(2x^2 - 3x + 2)\)[/tex].
### Step 1: Distribute Each Term
We'll distribute each term in [tex]\((3x + 5)\)[/tex] across each term in [tex]\((2x^2 - 3x + 2)\)[/tex].
1. Multiply [tex]\(3x\)[/tex] by each term in [tex]\(2x^2 - 3x + 2\)[/tex]:
- [tex]\(3x \cdot 2x^2 = 6x^3\)[/tex]
- [tex]\(3x \cdot (-3x) = -9x^2\)[/tex]
- [tex]\(3x \cdot 2 = 6x\)[/tex]
2. Multiply [tex]\(5\)[/tex] by each term in [tex]\(2x^2 - 3x + 2\)[/tex]:
- [tex]\(5 \cdot 2x^2 = 10x^2\)[/tex]
- [tex]\(5 \cdot (-3x) = -15x\)[/tex]
- [tex]\(5 \cdot 2 = 10\)[/tex]
### Step 2: Combine Like Terms
Now, we combine all the terms from the distribution:
- [tex]\(6x^3\)[/tex] (no other [tex]\(x^3\)[/tex] terms to combine with)
- [tex]\(-9x^2\)[/tex] and [tex]\(10x^2\)[/tex] combine to [tex]\(1x^2\)[/tex] or just [tex]\(x^2\)[/tex]
- [tex]\(6x\)[/tex] and [tex]\(-15x\)[/tex] combine to [tex]\(-9x\)[/tex]
- [tex]\(10\)[/tex] (stands alone)
### Step 3: Simplified Result
Putting it all together, the simplified expression is:
[tex]\[ 6x^3 + x^2 - 9x + 10 \][/tex]
And that's the simplified expression for [tex]\((3x + 5)(2x^2 - 3x + 2)\)[/tex].
We want to multiply and simplify the expression [tex]\((3x + 5)(2x^2 - 3x + 2)\)[/tex].
### Step 1: Distribute Each Term
We'll distribute each term in [tex]\((3x + 5)\)[/tex] across each term in [tex]\((2x^2 - 3x + 2)\)[/tex].
1. Multiply [tex]\(3x\)[/tex] by each term in [tex]\(2x^2 - 3x + 2\)[/tex]:
- [tex]\(3x \cdot 2x^2 = 6x^3\)[/tex]
- [tex]\(3x \cdot (-3x) = -9x^2\)[/tex]
- [tex]\(3x \cdot 2 = 6x\)[/tex]
2. Multiply [tex]\(5\)[/tex] by each term in [tex]\(2x^2 - 3x + 2\)[/tex]:
- [tex]\(5 \cdot 2x^2 = 10x^2\)[/tex]
- [tex]\(5 \cdot (-3x) = -15x\)[/tex]
- [tex]\(5 \cdot 2 = 10\)[/tex]
### Step 2: Combine Like Terms
Now, we combine all the terms from the distribution:
- [tex]\(6x^3\)[/tex] (no other [tex]\(x^3\)[/tex] terms to combine with)
- [tex]\(-9x^2\)[/tex] and [tex]\(10x^2\)[/tex] combine to [tex]\(1x^2\)[/tex] or just [tex]\(x^2\)[/tex]
- [tex]\(6x\)[/tex] and [tex]\(-15x\)[/tex] combine to [tex]\(-9x\)[/tex]
- [tex]\(10\)[/tex] (stands alone)
### Step 3: Simplified Result
Putting it all together, the simplified expression is:
[tex]\[ 6x^3 + x^2 - 9x + 10 \][/tex]
And that's the simplified expression for [tex]\((3x + 5)(2x^2 - 3x + 2)\)[/tex].
