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Use the table to answer the question.

A table is shown with 2 rows and 2 columns. The horizontal side is labeled 4 x cubed and 2 x squared while the vertical side is labeled 6 x and negative 9.

Find the product of (4x3+2x2)(6x−9)
. Provide your answer in descending order of exponents.

(1 point)
(4x3+2x2)(6x−9)=

1 answer

To find the product of \( (4x^3 + 2x^2)(6x - 9) \), we'll use the distributive property (also known as the FOIL method for binomials).

  1. Distribute \( 4x^3 \) to both terms in the second polynomial \( (6x - 9) \): \[ 4x^3 \cdot 6x = 24x^4 \] \[ 4x^3 \cdot (-9) = -36x^3 \]

  2. Distribute \( 2x^2 \) to both terms in the second polynomial \( (6x - 9) \): \[ 2x^2 \cdot 6x = 12x^3 \] \[ 2x^2 \cdot (-9) = -18x^2 \]

  3. Now, combine all the products obtained: \[ (4x^3 + 2x^2)(6x - 9) = 24x^4 - 36x^3 + 12x^3 - 18x^2 \]

  4. Combine like terms: \[ -36x^3 + 12x^3 = -24x^3 \]

  5. So, the complete expression is: \[ 24x^4 - 24x^3 - 18x^2 \]

Thus, the product is: \[ (4x^3 + 2x^2)(6x - 9) = 24x^4 - 24x^3 - 18x^2 \]