Question

Select the correct answer. Which expression is equivalent to the given polynomial expression? (9v^4 + 2) + v^2(v^2w^2 + 2w^3 - 2v^2) - (-13v^2w^3+7v^4)​

Answer 1

To find the equivalent expression, distribute v^2 to the terms within the second parentheses, remove parentheses, and combine like terms. The final simplified expression is 15v^2w^3 + v^4w^2 + 2.

Step-by-step explanation:

To find the equivalent expression for the given polynomial expression (9v^4 + 2) + v^2(v^2w^2 + 2w^3 - 2v^2) - (-13v^2w^3 + 7v^4), we will simplify the terms step by step. First, distribute the v^2 across the terms inside the second set of parentheses:

• v^2 * v^2w^2 = v^4w^2
• v^2 * 2w^3 = 2v^2w^3
• v^2 * (-2v^2) = -2v^4

After distributing, the expression looks like this:

(9v^4 + 2) + (v^4w^2 + 2v^2w^3 - 2v^4) - (-13v^2w^3 + 7v^4)

Next, remove the parentheses and simplify:

• 9v^4 + 2 + v^4w^2 + 2v^2w^3 - 2v^4 + 13v^2w^3 - 7v^4
• Combine like terms:
• (9v^4 - 2v^4 - 7v^4) + (2v^2w^3 + 13v^2w^3) + v^4w^2 + 2
• 0v^4 + 15v^2w^3 + v^4w^2 + 2

The final simplified expression is:

15v^2w^3 + v^4w^2 + 2