Expand (x - 1)(x - 2)(x - 3) to standard form.

Expand (x - 1)(x - 2)(x - 3) to standard form.

• A. x^3 - 5x^2 + 6x - 6
• B. x^3 - 6x^2 + 11x - 6
• C. x^3 - 6x^2 - 11x + 6
• D. x^3 - 6x^2 + x - 6

Answer: (B)

Expanding a product of three linear factors is done by multiplying two of them first to form a quadratic, then multiplying by the remaining one. Multiply (x − 1)(x − 2) to get x^2 − 3x + 2. Then multiply that by (x − 3): (x^2 − 3x + 2)(x − 3). Distribute: x^2·x = x^3, x^2·(−3) = −3x^2, (−3x)·x = −3x^2, (−3x)·(−3) = 9x, 2·x = 2x, 2·(−3) = −6. Combine like terms: x^3 − 6x^2 + 11x − 6. So the standard form is x^3 − 6x^2 + 11x − 6.

Expanding a product of three linear factors is done by multiplying two of them first to form a quadratic, then multiplying by the remaining one. Multiply (x − 1)(x − 2) to get x^2 − 3x + 2. Then multiply that by (x − 3): (x^2 − 3x + 2)(x − 3). Distribute: x^2·x = x^3, x^2·(−3) = −3x^2, (−3x)·x = −3x^2, (−3x)·(−3) = 9x, 2·x = 2x, 2·(−3) = −6. Combine like terms: x^3 − 6x^2 + 11x − 6. So the standard form is x^3 − 6x^2 + 11x − 6.