1

Problem

Simplify the expression \$ 5 + y^5 + 3y^2 - 9y^5 + y^3 - 7 - y^2\$.

2

Step

Given expression

\$ 5 + y^5 + 3y^2 - 9y^5 + y^3 - 7 - y^2\$

3

Step

Identify Like Terms:
Determine which terms in the expression involve the same variable(s) raised to the same power(s)

\$ y^5 \$ and \$-9y^5\$ , \$3y^2 \$ and \$-y^2\$

4

Step

Combine Like Terms:
Add or subtract the coefficients of like terms while keeping the variables unchanged

\$y^5 - y^5\$ + \$3y^2 - y^2\$ + 5 - 7

⇒ (1 - 9) \$y^5\$ + (3 - 1) \$y^2\$ - 2

⇒ \$ - 8y^5 + 2y^2\$ - 2

5

Hint

Bring in Other Terms:
Include any terms in the expression that do not involve like terms.

6

Solution

The simplified expression is \$-8y^5 + 2y^2 + y^3 - 2\$.

7

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

8

Choice-A

This option has the correct terms but with incorrect coefficients. It has \$4y^2\$ instead of \$2y^2\$, and the constant term is -2 instead of -7

Wrong \$-8y^5 + 4y^2 + y^3 - 2\$

9

Choice-B

This option has incorrect coefficients for the terms. It has \$6y^5\$ instead of \$-8y^5\$, and the constant term is -9 instead of -2

Wrong \$6y^5 + 2y^2 + y^3 - 9\$

10

Choice-C

This option has incorrect coefficients for the terms. It has \$8y^5\$ instead of \$-8y^5\$, and \$5y^2\$ instead of \$2y^2\$, and the constant term is -2 instead of -7

Wrong \$8y^5 + 5y^2 + y^3 - 2\$

11

Choice-D

This option has the correct terms and correct coefficients. It correctly simplifies the expression by grouping like terms together

Correct \$-8y^5 + 2y^2 + y^3 - 2\$

12

Step

Option

D

13

Sumup

Please Summarize Choices