Questions: Perform the indicated operation and simplify if possible by (3x-4)(x^2-6x-9)

Solution Steps

To solve the given expression, we need to perform polynomial multiplication. This involves distributing each term in the first polynomial, \(3x - 4\), across each term in the second polynomial, \(x^2 - 6x - 9\). After distributing, we combine like terms to simplify the expression.

To solve the expression \((3x - 4)(x^2 - 6x - 9)\), we begin by distributing each term in the first polynomial across each term in the second polynomial. This involves multiplying each term in \(3x - 4\) by each term in \(x^2 - 6x - 9\).

• Multiply \(3x\) by each term in \(x^2 - 6x - 9\):

  • \(3x \cdot x^2 = 3x^3\)
  • \(3x \cdot (-6x) = -18x^2\)
  • \(3x \cdot (-9) = -27x\)

• Multiply \(-4\) by each term in \(x^2 - 6x - 9\):

  • \(-4 \cdot x^2 = -4x^2\)
  • \(-4 \cdot (-6x) = 24x\)
  • \(-4 \cdot (-9) = 36\)

Combine the results from the multiplication:

• \(3x^3\)
• \(-18x^2 - 4x^2 = -22x^2\)
• \(-27x + 24x = -3x\)
• \(36\)

Final Answer