Simplify \$(9x^4 y^2 + 6 x^2 - 3y^3 + 24) + (- 15x^2 + 4x^4 y^2 + 8y^3 - 15)\$.

Given expressions:

\$9x^4 y^2 + 6 x^2 - 3y^3 + 24\$,

\$- 15x^2 + 4x^4 y^2 + 8y^3 - 15\$

Combine the terms involving \$x^4 y^2\$:

\$9x^4 y^2 + 4x^4 y^2\$

\$(9 + 4)x^4 y^2\$

\$13 x^4 y^2\$

Combine the terms involving \$x^2\$:

\$6 x^2 - 15 x^2\$

\$(6 - 15) x^2\$

\$-9 x^2\$

Combine the terms involving \$y^3\$:

\$-3 y^3 + 8 y^3\$

\$(-3 + 8)y^3\$

\$5 y^3\$

Combine the constant terms:

24 - 15 = 9

Putting it all together, we get:

\$13(x^4)(y^2) + 5(y^3) - 9(x^2) + 9\$

So, the simplified expression is \$13(x^4)(y^2) + 5(y^3) - 9(x^2) + 9\$.

All terms and their coefficients are correctly placed So, This option matches the given simplified expression perfectly

\$13(x^4)(y^2) + 5(y^3) - 9(x^2) + 9\$

This option has incorrect coefficients for \$y^3\$ and the constant term. It should be \$5y^3\$ instead of \$9y^3\$ and 9 instead of 5

\$13(x^4)(y^2) + 9(y^3) - 9(x^2) + 5\$

This option has the incorrect sign for the \$y^3\$ term. It should be \$+5y^3\$ instead of \$−5y^3\$

\$13(x^4)(y^2) - 5(y^3) - 9(x^2) + 9\$

This option has incorrect signs for all terms. The coefficients of \$x^4 y^2\$ and \$y^3\$ have incorrect signs

\$-13(x^4)(y^2) - 9(y^3) - 9(x^2) - 5\$

Option

A

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