Expand the expression to a polynomial in standard form:

Question

Expand the expression to a polynomial in standard form:
left parenthesis, 4, x, minus, 3, right parenthesis, left parenthesis, minus, 3, x, squared, minus, 8, x, plus, 1, right parenthesis
(4x−3)(−3x 
2
 −8x+1)

Solve the problem just like the example below
                                     ⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, 4, x, minus, 3, right parenthesis, left parenthesis, 2, x, squared, minus, 2, x, minus, 5, right parenthesis

(4x−3)(2x
2
−2x−5)

Combine like terms:
              8x³- 14x²-14x+15

GPT-4o mini · Answer

To expand the expression $(4x - 3)(-3x^2 - 8x + 1)$ and write it in standard form, we will use the distributive property (also known as the FOIL method for binomials). ### Step 1: Distribute $4x$ to each term in the second polynomial: $$ 4x \cdot (-3x^2) = -12x^3 $$ $$ 4x \cdot (-8x) = -32x^2 $$ $$ 4x \cdot (1) = 4x $$ ### Step 2: Distribute $-3$ to each term in the second polynomial: $$ -3 \cdot (-3x^2) = 9x^2 $$ $$ -3 \cdot (-8x) = 24x $$ $$ -3 \cdot (1) = -3 $$ ### Step 3: Combine all the results together: Now we have: $$ -12x^3 - 32x^2 + 4x + 9x^2 + 24x - 3 $$ ### Step 4: Combine like terms: - For $x^3$ terms: $-12x^3$ - For $x^2$ terms: $-32x^2 + 9x^2 = -23x^2$ - For $x$ terms: $4x + 24x = 28x$ - Constant term: $-3$ ### Final Result: Putting it all together, we get: $$ -12x^3 - 23x^2 + 28x - 3 $$ Thus, the expanded expression in standard form is: $$ \boxed{-12x^3 - 23x^2 + 28x - 3} $$

Expand the expression to a polynomial in standard form:

Step 1: Distribute \(4x\) to each term in the second polynomial:

Step 2: Distribute \(-3\) to each term in the second polynomial:

Step 3: Combine all the results together:

Step 4: Combine like terms:

Final Result: