(2x%5E2-7x%2B1).jpeg "(3x-6)(2x^2-7x+1)")
Expanding the Expression (3x-6)(2x^2-7x+1)
This article will guide you through the process of expanding the expression (3x-6)(2x^2-7x+1). We will utilize the distributive property, often referred to as the FOIL method, to achieve this.
Understanding the FOIL Method
FOIL stands for First, Outer, Inner, Last. It's a mnemonic device used to remember the steps involved in multiplying two binomials. Here's how it works:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's apply the FOIL method to our expression (3x-6)(2x^2-7x+1):
- First: (3x) * (2x^2) = 6x^3
- Outer: (3x) * (-7x) = -21x^2
- Inner: (-6) * (2x^2) = -12x^2
- Last: (-6) * (-7x) = 42x
- Last: (-6) * (1) = -6
Now we combine all the terms:
6x^3 - 21x^2 - 12x^2 + 42x - 6
Finally, we combine the like terms:
6x^3 - 33x^2 + 42x - 6
Conclusion
By applying the FOIL method, we successfully expanded the expression (3x-6)(2x^2-7x+1) into a polynomial of degree 3. The final expanded form is 6x^3 - 33x^2 + 42x - 6.