(x-3)(x-2)-in-standard-form.jpeg "(2x+1)(x-3)(x-2) In Standard Form")
Expanding and Simplifying (2x+1)(x-3)(x-2) into Standard Form
This article will guide you through the process of expanding and simplifying the expression (2x+1)(x-3)(x-2) into its standard polynomial form.
Step 1: Expand the first two factors
We'll start by multiplying the first two factors, (2x+1) and (x-3), using the distributive property (also known as FOIL):
(2x+1)(x-3) = 2x(x-3) + 1(x-3)
Expanding further:
= 2x² - 6x + x - 3
= 2x² - 5x - 3
Step 2: Multiply the result with the remaining factor
Now we'll multiply the simplified expression (2x² - 5x - 3) with the remaining factor (x-2):
(2x² - 5x - 3)(x-2) = 2x²(x-2) - 5x(x-2) - 3(x-2)
Expanding:
= 2x³ - 4x² - 5x² + 10x - 3x + 6
Step 3: Combine like terms
Finally, we'll combine the like terms to get the expression in its standard polynomial form:
= 2x³ - 9x² + 7x + 6
Conclusion
Therefore, the standard form of the expression (2x+1)(x-3)(x-2) is 2x³ - 9x² + 7x + 6.