Question

Expand the expression to a polynomial in standard form:
left parenthesis, 3, x, minus, 1, right parenthesis, left parenthesis, x, squared, plus, 9, x, plus, 4, right parenthesis
(3x−1)(x
2
+9x+4)


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 \((3x - 1)(x^2 + 9x + 4)\) and write it in standard form, we'll distribute each term in the first expression to each term in the second expression.

### Step 1: Distribute \(3x\) to each term in \((x^2 + 9x + 4)\)

1. \(3x \cdot x^2 = 3x^3\)
2. \(3x \cdot 9x = 27x^2\)
3. \(3x \cdot 4 = 12x\)

This gives us:
\[
3x^3 + 27x^2 + 12x
\]

### Step 2: Distribute \(-1\) to each term in \((x^2 + 9x + 4)\)

1. \(-1 \cdot x^2 = -x^2\)
2. \(-1 \cdot 9x = -9x\)
3. \(-1 \cdot 4 = -4\)

This gives us:
\[
-x^2 - 9x - 4
\]

### Step 3: Combine the results

Now we can combine all the terms:
\[
3x^3 + 27x^2 + 12x - x^2 - 9x - 4
\]

### Step 4: Combine like terms

1. Combine \(27x^2\) and \(-x^2\):
\[
27x^2 - x^2 = 26x^2
\]

2. Combine \(12x\) and \(-9x\):
\[
12x - 9x = 3x
\]

3. The constant term is -4.

Putting it all together, we get:
\[
3x^3 + 26x^2 + 3x - 4
\]

### Final Answer

The expanded polynomial in standard form is:
\[
3x^3 + 26x^2 + 3x - 4
\]