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

Answer 1

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:

\[
\boxed{-12x^3 - 23x^2 + 28x - 3}
\]