which expression is equivalent to x^3(2+y^5)

Answer 1

The expression \( x^3(2 + y^5) \) can be considered in its original form. However, if you're looking for an alternate representation by distributing \( x^3 \) over the terms inside the parentheses, you can expand it:

\[ x^3(2 + y^5) = x^3 \cdot 2 + x^3 \cdot y^5 \]

This can be written as:

\[ 2x^3 + x^3y^5 \]

So, both \( x^3(2 + y^5) \) and \( 2x^3 + x^3y^5 \) are equivalent expressions.

Answer 2

(1/2x^2-3)(4y^3+5x^2)

Answer 3

To expand the expression \((\frac{1}{2}x^2 - 3)(4y^3 + 5x^2)\), we will apply the distributive property (also known as the FOIL method for binomials). We'll multiply each term in the first parentheses by each term in the second parentheses.

1. Multiply \(\frac{1}{2}x^2\) by \(4y^3\): \[ \frac{1}{2}x^2 \cdot 4y^3 = 2x^2y^3 \]

2. Multiply \(\frac{1}{2}x^2\) by \(5x^2\): \[ \frac{1}{2}x^2 \cdot 5x^2 = \frac{5}{2}x^4 \]

3. Multiply \(-3\) by \(4y^3\): \[ -3 \cdot 4y^3 = -12y^3 \]

4. Multiply \(-3\) by \(5x^2\): \[ -3 \cdot 5x^2 = -15x^2 \]

Now we can combine all these results to get the expanded form:

\[ 2x^2y^3 + \frac{5}{2}x^4 - 12y^3 - 15x^2 \]

Thus, the fully expanded form of \((\frac{1}{2}x^2 - 3)(4y^3 + 5x^2)\) is:

\[ \frac{5}{2}x^4 + 2x^2y^3 - 15x^2 - 12y^3 \]