Question

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

Answer 1

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

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

Calculating each term:

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

Now we combine all the terms together:

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

Next, we combine like terms:

- The \( x^2 \) terms: \( 3x^2 - 6x^2 = -3x^2 \)

So we have:

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

Now, rewriting the final expression in standard form gives us:

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

Thus, the answer is:

**5x³ − 3x² − 7x**