Expand the expression to a polynomial in standard form:

Question

left parenthesis, 3, x, plus, 8, right parenthesis, left parenthesis, 3, x, squared, plus, x, minus, 1, right parenthesis
(3x+8)(3x
2
+x−1)

Answer 1

To expand the expression \((3x + 8)(3x^2 + x - 1)\), we'll use the distributive property (also known as the FOIL method for binomials). We'll multiply each term in the first polynomial by each term in the second polynomial.

1. Multiply \(3x\) by each term in \(3x^2 + x - 1\):

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

   So, this part gives us: \[ 9x^3 + 3x^2 - 3x \]

2. Multiply \(8\) by each term in \(3x^2 + x - 1\):

   • \(8 \cdot 3x^2 = 24x^2\)
   • \(8 \cdot x = 8x\)
   • \(8 \cdot (-1) = -8\)

   So, this part gives us: \[ 24x^2 + 8x - 8 \]

3. Combine all the terms together: \[ 9x^3 + 3x^2 - 3x + 24x^2 + 8x - 8 \]

4. Combine like terms:

   • \(9x^3\)
   • Combine \(3x^2 + 24x^2 = 27x^2\)
   • Combine \(-3x + 8x = 5x\)
   • The constant term is \(-8\)

So, the complete expanded expression is: \[ \boxed{9x^3 + 27x^2 + 5x - 8} \]