Expand the expression to a polynomial in standard form:

Question

left parenthesis, 3, x, plus, 1, right parenthesis, left parenthesis, 3, x, squared, plus, 7, x, minus, 7, right parenthesis
(3x+1)(3x
2
+7x−7)

Answer 1

To expand the expression \((3x + 1)(3x^2 + 7x - 7)\), we will use the distributive property (also known as the FOIL method in the case of binomials).

1. Distribute \(3x\) to each term in the second polynomial: \[ 3x \cdot 3x^2 = 9x^3 \] \[ 3x \cdot 7x = 21x^2 \] \[ 3x \cdot (-7) = -21x \]

2. Distribute \(1\) to each term in the second polynomial: \[ 1 \cdot 3x^2 = 3x^2 \] \[ 1 \cdot 7x = 7x \] \[ 1 \cdot (-7) = -7 \]

3. Combine all the results: \[ 9x^3 + 21x^2 - 21x + 3x^2 + 7x - 7 \]

4. Combine like terms:

   • For \(x^2\) terms: \(21x^2 + 3x^2 = 24x^2\)
   • For \(x\) terms: \(-21x + 7x = -14x\)

So, the expression simplifies to: \[ 9x^3 + 24x^2 - 14x - 7 \]

The final answer in standard form is: \[ \boxed{9x^3 + 24x^2 - 14x - 7} \]