Expand the expression to a polynomial in standard form:

Question

left parenthesis, 4, x, minus, 1, right parenthesis, left parenthesis, minus, 3, x, squared, minus, 2, x, minus, 6, right parenthesis
(4x−1)(−3x
2
−2x−6)

Answer 1

To expand the expression $(4x-1)(-3x^2-2x-6)$, we will use the distributive property (also known as the FOIL method for binomials). Here’s how it works step by step:

1. Distribute $4x$ over $-3x^2-2x-6$: $$4x(-3x^2)+4x(-2x)+4x(-6)=-12x^3-8x^2-24x$$

2. Distribute $-1$ over $-3x^2-2x-6$: $$-1(-3x^2)+(-1)(-2x)+(-1)(-6)=3x^2+2x+6$$

3. Combine the results from step 1 and step 2: $$-12x^3-8x^2-24x+3x^2+2x+6$$

4. Combine like terms:

   • For $x^3$ terms: $-12x^3$
   • For $x^2$ terms: $-8x^2+3x^2=-5x^2$
   • For $x$ terms: $-24x+2x=-22x$
   • For constant terms: $6$

Thus, the expanded polynomial in standard form is: $$-12x^3-5x^2-22x+6$$