Here are the simplified expressions for each problem. I have combined the "like terms" (terms that have the exact same variables and powers) to get the final answers.
1.
$4ax - 5ax + 4$
* Combine $4ax$ and $-5ax$: $(4 - 5)ax = -1ax$ or $-ax$.
* The constant $+4$ stays as it is.
* Result: $-ax + 4$
2.
$12ax^2 - 8ax^2 + 4$
* Combine $12ax^2$ and $-8ax^2$: $(12 - 8)ax^2 = 4ax^2$.
* The constant $+4$ stays as it is.
* Result: $4ax^2 + 4$
3.
$4a^2x - 5a^2x + 4y - 9y$
* Combine $a^2x$ terms: $4 - 5 = -1$, so $-a^2x$.
* Combine $y$ terms: $4 - 9 = -5$, so $-5y$.
* Result: $-a^2x - 5y$
4.
$-3y^2x + 6xy^2 - 2y - 7y$
* Note that $y^2x$ is the same as $xy^2$. Combine $-3xy^2$ and $6xy^2$: $-3 + 6 = 3$, so $3xy^2$ (or $3y^2x$).
* Combine $y$ terms: $-2 - 7 = -9$, so $-9y$.
* Result: $3y^2x - 9y$
5.
$6m^2n^3 - 12mn - 5mn - 8m^2n^3$
* Combine $m^2n^3$ terms: $6 - 8 = -2$, so $-2m^2n^3$.
* Combine $mn$ terms: $-12 - 5 = -17$, so $-17mn$.
* Result: $-2m^2n^3 - 17mn$
6.
$-21mn + 4f - 2f - 5mn$
* Combine $mn$ terms: $-21 - 5 = -26$, so $-26mn$.
* Combine $f$ terms: $4 - 2 = 2$, so $+2f$.
* Result: $-26mn + 2f$
7.
$7x^2y - xy^2 - 5x^2y - 2xy^2$
* Combine $x^2y$ terms: $7 - 5 = 2$, so $2x^2y$.
* Combine $xy^2$ terms: $-1 - 2 = -3$, so $-3xy^2$.
* Result: $2x^2y - 3xy^2$
8.
$3xy + 8yx - 5 + 4$
* Note that $xy$ is the same as $yx$. Combine them: $3 + 8 = 11$, so $11xy$.
* Combine constants: $-5 + 4 = -1$.
* Result: $11xy - 1$
9.
$10x - 4 + 5 + x$
* Combine $x$ terms: $10x + 1x = 11x$.
* Combine constants: $-4 + 5 = 1$.
* Result: $11x + 1$
10.
$-3a^2x^2 + 5a^2x^2 + 4y - 3y$
* Combine $a^2x^2$ terms: $-3 + 5 = 2$, so $2a^2x^2$.
* Combine $y$ terms: $4 - 3 = 1$, so $+y$.
* Result: $2a^2x^2 + y$
Final Answer:
1. $-ax + 4$
2. $4ax^2 + 4$
3. $-a^2x - 5y$
4. $3y^2x - 9y$
5. $-2m^2n^3 - 17mn$
6. $-26mn + 2f$
7. $2x^2y - 3xy^2$
8. $11xy - 1$
9. $11x + 1$
10. $2a^2x^2 + y$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting expressions worksheet.
