Polynomials — simplification with all four operations

Like terms must have exactly the same variable(s) raised to exactly the same power(s). Only the coefficients (numbers in front) may differ.

$4x^2$ and $4x$ differ in power ($x^2$ vs $x^1$). $3ab$ and $3a$ differ because one has $b$. $5m$ and $5n$ have different variables.

Both $7y^2$ and $-2y^2$ have the variable $y$ raised to the power $2$. They are like terms — their coefficients ($7$ and $-2$) are different, but that is fine.

We need to find the pair where both terms share the same variable(s) with the same exponent(s).

These are not like terms. $4x^2$ has power 2, but $4x$ has power 1 — the exponents do not match.

These are not like terms. $3ab$ contains both $a$ and $b$, while $3a$ only contains $a$. The variable parts are different.

These are not like terms because they have different variable letters: $m$ and $n$.

Both terms have exactly $y^2$, so they are like terms. The correct answer is $7y^2$ and $-2y^2$.

The $x$-terms are $8x$ and $-5x$. The $y$-terms are $3y$ and $2y$.

$8x-5x=(8-5)x=3x$

$3y+2y=(3+2)y=5y$

$3x+5y$ This is fully simplified because $x$-terms and $y$-terms are unlike terms and cannot be combined.

Combining $x$-terms: $8x-5x=3x$. Combining $y$-terms: $3y+2y=5y$. So the answer should be $3x+5y$.

$13x$ would come from adding $8x+5x$, but we need $8x-5x$. This answer incorrectly adds instead of subtracting.

The $y$-terms are $+3y$ and $+2y$, which give $+5y$, not $-5y$. This option has the wrong sign on the $y$-term.

$3y+2y=5y$, not $y$. This option incorrectly subtracts the $y$-coefficients.

This is the only option with both correct parts: $3x$ and $5y$.