Expand the expression to a polynomial in standard form:

Question

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: \[ 3x^3 + 26x^2 + 3x - 4 \]