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

Given expression

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

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

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

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

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

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

⇒ \$ - 8"y"^5 + "y"^3 + 2"y"^2 - 2\$

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

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

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

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

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

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

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

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

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

Option

D

Can you summarize what you’ve understood in the above steps?