Question

expand the expression to a polynomial in standard form:
$(2x - 3)(3x^2 - x + 6)$

Explanation:

Step1: Distribute $2x$ to each term

$2x \cdot 3x^2 + 2x \cdot (-x) + 2x \cdot 6 = 6x^3 - 2x^2 + 12x$

Step2: Distribute $-3$ to each term

$-3 \cdot 3x^2 + (-3) \cdot (-x) + (-3) \cdot 6 = -9x^2 + 3x - 18$

Step3: Combine all expanded terms

$6x^3 - 2x^2 + 12x - 9x^2 + 3x - 18$

Step4: Combine like terms

$6x^3 + (-2x^2 -9x^2) + (12x + 3x) - 18 = 6x^3 -11x^2 +15x -18$

Answer:

$6x^3 - 11x^2 + 15x - 18$