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Use the distributive property to find the product of x(3x +5x2−7−6x) . Write your answer in standard form.(1 point) Responses 5x3−3x2+7x 5 x cubed minus 3 x squared plus 7 x 5x2−3x−7 5 x squared minus 3 x minus 7 −7x + 5x3−3x2 −7x + 5x3−3x2 5x3−3x2−7x 5 x cubed minus 3 x squared minus 7 x 3x2+5x3−7x − 6x2 3x2+5x3−7x − 6x2 5x3+3x2+7x 5 x cubed plus 3 x squared plus 7 x 5x3−9x2+7x

1 answer

To find the product of \( x(3x + 5x^2 - 7 - 6x) \) using the distributive property, we distribute \( x \) to each term inside the parentheses:

  1. \( x \cdot 3x = 3x^2 \)
  2. \( x \cdot 5x^2 = 5x^3 \)
  3. \( x \cdot (-7) = -7x \)
  4. \( x \cdot (-6x) = -6x^2 \)

Now we combine these results:

\[ 5x^3 + 3x^2 - 7x - 6x^2 \]

Combining the like terms \( 3x^2 \) and \( -6x^2 \):

\[ 5x^3 + (3x^2 - 6x^2) - 7x = 5x^3 - 3x^2 - 7x \]

So, the expression in standard form is:

\[ 5x^3 - 3x^2 - 7x \]

The correct response is:

5x³ - 3x² - 7x