(x%2B2)(x%E2%88%921)(x%2B3).jpeg "(x+3)(x+2)(x−1)(x+3)")
Expanding and Simplifying (x+3)(x+2)(x−1)(x+3)
This expression involves multiplying four binomials together. We can simplify it step by step using the distributive property (also known as FOIL).
Step 1: Multiply the first two binomials
(x+3)(x+2) = x(x+2) + 3(x+2) = x² + 2x + 3x + 6 = x² + 5x + 6
Step 2: Multiply the last two binomials
(x−1)(x+3) = x(x+3) -1(x+3) = x² + 3x - x - 3 = x² + 2x - 3
Step 3: Multiply the results from Step 1 and Step 2
(x² + 5x + 6)(x² + 2x - 3) = x²(x² + 2x - 3) + 5x(x² + 2x - 3) + 6(x² + 2x - 3)
Now, we distribute each term outside the parentheses:
= x⁴ + 2x³ - 3x² + 5x³ + 10x² - 15x + 6x² + 12x - 18
Step 4: Combine like terms
= x⁴ + (2x³ + 5x³) + (-3x² + 10x² + 6x²) + (-15x + 12x) - 18
= x⁴ + 7x³ + 13x² - 3x - 18
Therefore, the simplified form of the expression (x+3)(x+2)(x−1)(x+3) is x⁴ + 7x³ + 13x² - 3x - 18.