Use the distributive property to find the product of x(2 - 3x + 4xy - 7). Write your answer in standard form.

Answer 1

To find the product of \( x(2 - 3x + 4xy - 7) \) using the distributive property, we will distribute \( x \) to each term inside the parentheses:

\[ x(2) + x(-3x) + x(4xy) + x(-7) \]

Now, we can calculate each term:

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

Now, we combine these results:

\[ 2x - 3x^2 + 4xy - 7x \]

Next, we combine like terms, specifically the \( x \) terms \( 2x \) and \( -7x \):

\[ (2x - 7x) - 3x^2 + 4xy = -5x - 3x^2 + 4xy \]

To write it in standard form, we typically place the terms in descending order of their degrees. The standard form for this expression is:

\[ -3x^2 + 4xy - 5x \]

Thus, the final answer is:

\[ -3x^2 + 4xy - 5x \]