Expand the expression to a polynomial in standard form:

Question

Expand the expression to a polynomial in standard form:
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)

GPT-4o mini · Answer

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: $$ -12x^3 - 5x^2 - 22x + 6 $$