(x%E2%88%921)(2x%2B1)(x%2B6).jpeg "(x+2)(x−1)(2x+1)(x+6)")
Expanding and Simplifying (x+2)(x−1)(2x+1)(x+6)
This article explores how to expand and simplify the given expression: (x+2)(x−1)(2x+1)(x+6). We'll utilize the distributive property and combine like terms to arrive at a simplified polynomial form.
Step 1: Expand the first two factors.
First, we'll multiply the first two factors, (x+2)(x−1) using the FOIL method (First, Outer, Inner, Last):
(x+2)(x−1) = x² - x + 2x - 2 = x² + x - 2
Step 2: Expand the last two factors.
Similarly, we'll multiply the last two factors, (2x+1)(x+6):
(2x+1)(x+6) = 2x² + 12x + x + 6 = 2x² + 13x + 6
Step 3: Expand the resulting expressions.
Now, we have the expression: (x² + x - 2)(2x² + 13x + 6). Let's expand this by multiplying each term in the first expression by each term in the second expression.
x² * (2x² + 13x + 6) = 2x⁴ + 13x³ + 6x² x * (2x² + 13x + 6) = 2x³ + 13x² + 6x -2 * (2x² + 13x + 6) = -4x² - 26x - 12
Step 4: Combine like terms.
Finally, we add all the resulting terms together and combine like terms:
2x⁴ + 13x³ + 6x² + 2x³ + 13x² + 6x - 4x² - 26x - 12
= 2x⁴ + 15x³ + 15x² - 20x - 12
Therefore, the simplified form of the expression (x+2)(x−1)(2x+1)(x+6) is 2x⁴ + 15x³ + 15x² - 20x - 12.