Use the distributive property to find the product of x(2x + 4x^2 - 5 - 3x).

Question

Write your answer in standard form.

Answer 1

To find the product of \( x(2x + 4x^2 - 5 - 3x) \) using the distributive property, we will distribute \( x \) to each term inside the parentheses.

1. Distribute \( x \) to \( 2x \): \[ x \cdot 2x = 2x^2 \]
2. Distribute \( x \) to \( 4x^2 \): \[ x \cdot 4x^2 = 4x^3 \]
3. Distribute \( x \) to \( -5 \): \[ x \cdot (-5) = -5x \]
4. Distribute \( x \) to \( -3x \): \[ x \cdot (-3x) = -3x^2 \]

Now, we combine all the terms: \[ 4x^3 + 2x^2 - 5x - 3x^2 \]

Next, we combine like terms:

• The \( x^2 \) terms: \( 2x^2 - 3x^2 = -1x^2 \) or simply \( -x^2 \).

So, we have: \[ 4x^3 - x^2 - 5x \]

Finally, we write the answer in standard form, which is organizing the terms by descending powers of \( x \): \[ \boxed{4x^3 - x^2 - 5x} \]