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Use the Distributive Property to rewrite the expression (xβˆ’2)(8x+6)(π‘₯βˆ’2)(8π‘₯+6). (1 point)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.Response areax2π‘₯2 βˆ’βˆ’ Response areaxπ‘₯ βˆ’βˆ’ Response area81012

1 answer

To use the Distributive Property to rewrite the expression \((x - 2)(8x + 6)\), we need to apply the distributive property (also known as the FOIL method for binomials).

  1. Distribute \(x\) to both terms in the second binomial: \[ x \cdot 8x + x \cdot 6 = 8x^2 + 6x \]

  2. Distribute \(-2\) to both terms in the second binomial: \[ -2 \cdot 8x + (-2) \cdot 6 = -16x - 12 \]

  3. Now combine all the terms together: \[ 8x^2 + 6x - 16x - 12 \]

  4. Combine like terms: \[ 8x^2 + (6x - 16x) - 12 = 8x^2 - 10x - 12 \]

Thus, the rewritten expression using the Distributive Property is: \[ 8x^2 - 10x - 12 \]

From your description, it seems you have specific response areas for \(x^2\), \(x\), and constants:

  • \(8\) for \(x^2\)
  • \(-10\) for \(x\)
  • \(-12\) for the constant.

Fill in the respective response areas with these numbers.