(5%E2%88%922x)(4x%2B1).jpeg "(3x−4)(5−2x)(4x+1)")
Expanding and Simplifying the Expression (3x−4)(5−2x)(4x+1)
This article will guide you through the steps of expanding and simplifying the expression (3x−4)(5−2x)(4x+1).
Step 1: Expand the First Two Factors
First, we'll focus on multiplying the first two factors: (3x−4)(5−2x).
To do this, we'll use the FOIL method:
- First: (3x)(5) = 15x
- Outer: (3x)(-2x) = -6x²
- Inner: (-4)(5) = -20
- Last: (-4)(-2x) = 8x
Combining these terms, we get:
(3x−4)(5−2x) = 15x - 6x² - 20 + 8x
Simplifying this further:
(3x−4)(5−2x) = -6x² + 23x - 20
Step 2: Multiply the Result by the Third Factor
Now, we need to multiply this simplified expression by the third factor: (4x+1)
This is similar to the previous step, but now we're multiplying a trinomial by a binomial. We'll distribute each term in the trinomial by the binomial:
- -6x² (4x+1) = -24x³ - 6x²
- 23x (4x+1) = 92x² + 23x
- -20 (4x+1) = -80x - 20
Combining these terms:
(-6x² + 23x - 20)(4x+1) = -24x³ - 6x² + 92x² + 23x - 80x - 20
Step 3: Simplify the Expression
Finally, we combine like terms to simplify the expression:
-24x³ + 86x² - 57x - 20
Conclusion
Therefore, the expanded and simplified form of the expression (3x−4)(5−2x)(4x+1) is -24x³ + 86x² - 57x - 20.