Explanation:
We are adding monomials. Remember:
You can only add monomials that are like terms, meaning they have the exact same variables raised to the exact same powers.
Let’s go one by one:
1) $-ab + 4ab$
Both have $ab$, so combine coefficients: $-1 + 4 = 3$ →
$3ab$
2) $5m^3 + (-22n^3)$
$m^3$ and $n^3$ are *not* like terms (different variables), so we cannot combine them.
Answer:
$5m^3 - 22n^3$ (just write as is — no simplification)
3) $-4pq^2 + (-2pq^2)$
Same variables: $pq^2$. Coefficients: $-4 + (-2) = -6$ →
$-6pq^2$
4) $2x^3y^2 + 6x^3y^2$
Same: $x^3y^2$. Coefficients: $2 + 6 = 8$ →
$8x^3y^2$
5) $3u + (-3uv)$
First term: $3u$, second: $-3uv$ — different! One has just $u$, the other has $uv$. Not like terms.
Answer:
$3u - 3uv$ (no combining)
6) $-17n^2t^3 + (-12n^2t^3)$
Same: $n^2t^3$. Coefficients: $-17 + (-12) = -29$ →
$-29n^2t^3$
7) $15c^2d + 25c^2d$
Same: $c^2d$. Coefficients: $15 + 25 = 40$ →
$40c^2d$
8) $-5g + 8h$
Different variables: $g$ vs $h$. Not like terms.
Answer:
$-5g + 8h$
9) $11y^2z^3 + (-7z^3)$
First: $y^2z^3$, second: $z^3$ — missing $y^2$ in second term, so not like terms.
Answer:
$11y^2z^3 - 7z^3$
10) $b^3cd^4 + b^3cd^4$
Exactly the same! Coefficients: $1 + 1 = 2$ →
$2b^3cd^4$
Let me double-check each:
1)
✔ $-ab + 4ab = 3ab$
2)
✔ $5m^3 - 22n^3$ — can’t combine
3)
✔ $-4pq^2 - 2pq^2 = -6pq^2$
4)
✔ $2x^3y^2 + 6x^3y^2 = 8x^3y^2$
5)
✔ $3u - 3uv$ — different
6)
✔ $-17 -12 = -29$ → $-29n^2t^3$
7)
✔ $15+25=40$ → $40c^2d$
8)
✔ $-5g + 8h$ — different
9)
✔ $11y^2z^3 - 7z^3$ — not like terms
10)
✔ $1+1=2$ → $2b^3cd^4$
All correct.
Final Answer:
1) $3ab$
2) $5m^3 - 22n^3$
3) $-6pq^2$
4) $8x^3y^2$
5) $3u - 3uv$
6) $-29n^2t^3$
7) $40c^2d$
8) $-5g + 8h$
9) $11y^2z^3 - 7z^3$
10) $2b^3cd^4$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting monomials worksheet.
