Final answer:
To find the product of (2x - 3)(x + 4)(x - 1), first multiply (x + 4) and (x - 1), then multiply the result by (2x - 3), and finally combine like terms to get the simplified expression 2x³ + 3x² - 17x + 12.
Step-by-step explanation:
To perform the multiplication and combine like terms for the given expression (2x – 3)(x + 4)(x – 1), we proceed step by step. Firstly, we can multiply the binomials (x + 4) and (x – 1) using the FOIL method, and then multiply the resulting expression by (2x – 3). After the multiplication, we combine like terms which have the same variable to the same power.
Multiplying the binomials:
(x + 4)(x – 1) = x(x) + x(-1) + 4(x) + 4(-1) = x² – x + 4x – 4 = x² + 3x – 4
Now, we multiply this result by (2x – 3):
(2x – 3)(x² + 3x – 4) = 2x(x²) + 2x(3x) + 2x(-4) – 3(x²) – 3(3x) – 3(-4) = 2x³ + 6x² - 8x - 3x² - 9x + 12
Combine like terms:
2x³ + (6x² - 3x²) + (-8x - 9x) + 12 = 2x³ + 3x² - 17x + 12
The final simplified expression after multiplication and combining like terms is 2x³ + 3x² - 17x + 12.