Let's break down the expression step by step:
The expression you provided is:
\[ 5(x^2 - 4x + 4)x - 2 + (x + 1)(x^2 - x + 3) \]
Step 1: Simplify \(5(x^2 - 4x + 4)x - 2\)
First, we will distribute \(5\) and then multiply by \(x\):
\[ 5(x^2 - 4x + 4)x = 5x(x^2 - 4x + 4) = 5x^3 - 20x^2 + 20x \]
Now, subtract \(2\):
\[ 5x^3 - 20x^2 + 20x - 2 \]
Step 2: Simplify \((x + 1)(x^2 - x + 3)\)
Now we will distribute \((x + 1)\) across \((x^2 - x + 3)\):
\[ (x + 1)(x^2 - x + 3) = x(x^2 - x + 3) + 1(x^2 - x + 3) \]
Calculating this out gives:
\[ = x^3 - x^2 + 3x + x^2 - x + 3 = x^3 + 2x + 3 \]
Step 3: Combine the Simplified Parts
Now combine everything:
\[ 5x^3 - 20x^2 + 20x - 2 + x^3 + 2x + 3 \]
Combine like terms:
- For \(x^3\): \(5x^3 + x^3 = 6x^3\)
- For \(x^2\): \(-20x^2\)
- For \(x\): \(20x + 2x = 22x\)
- For the constant: \(-2 + 3 = 1\)
Putting it all together:
\[ 6x^3 - 20x^2 + 22x + 1 \]
Now let's look at the original provided options again. None of these options match (as we simplified to \(6x^3 - 20x^2 + 22x + 1\)). We reconsider possibility of scaling, or if there's an error in the options or calculations.
Final expression in ordered polynomial form would be:
\[ 6x^3 - 20x^2 + 22x + 1 \]
Which still does not appear in the responses given. Could you please double-check the math and clarify if that was the intended problem?
1 answer