Adding+Subtracting Polynomials | PDF - Free Printable

Here are the simplified expressions for each problem on the worksheet.

1) $(5y^2 - 2) + (2y^2 - 3)$
Combine like terms: $5y^2 + 2y^2 = 7y^2$ and $-2 - 3 = -5$.
Answer: $7y^2 - 5$

2) $(a^3 - 2a^2) - (3a^3 - 4a^2)$
Distribute the negative sign: $a^3 - 2a^2 - 3a^3 + 4a^2$.
Combine like terms: $a^3 - 3a^3 = -2a^3$ and $-2a^2 + 4a^2 = 2a^2$.
Answer: $-2a^3 + 2a^2$

3) $(4 + 2x^3) + (5x^3 + 2)$
Combine like terms: $2x^3 + 5x^3 = 7x^3$ and $4 + 2 = 6$.
Answer: $7x^3 + 6$

4) $(4a - 3a^2) - (3a^3 + 4a)$
Distribute the negative sign: $4a - 3a^2 - 3a^3 - 4a$.
Combine like terms: $4a - 4a = 0$. The remaining terms are $-3a^3 - 3a^2$.
Answer: $-3a^3 - 3a^2$

5) $(3a^2 + 1) + (4 + 2a^3)$
Rearrange and combine: $2a^3 + 3a^2 + 1 + 4$.
Answer: $2a^3 + 3a^2 + 5$

6) $(4b^3 + 3b^2) - (s^3 - 5s^2)$
*Note: The variables in the second parenthesis appear to be 's' based on the image, while the first are 'b'. If they are different variables, they cannot be combined.*
Distribute the negative sign: $4b^3 + 3b^2 - s^3 + 5s^2$.
Answer: $4b^3 + 3b^2 - s^3 + 5s^2$
*(If the second part was meant to be $b^3 - 5b^2$, the answer would be $3b^3 + 8b^2$)*

7) $(5a + 4) - (5a + 3)$
Distribute the negative sign: $5a + 4 - 5a - 3$.
Combine like terms: $5a - 5a = 0$ and $4 - 3 = 1$.
Answer: $1$

8) $(3x^2 + 3) - (3x - 5x^2)$
Distribute the negative sign: $3x^2 + 3 - 3x + 5x^2$.
Combine like terms: $3x^2 + 5x^2 = 8x^2$. The $-3x$ and $+3$ remain.
Answer: $8x^2 - 3x + 3$

9) $(-4k^2 + 4) + (k^3) + (-3k^2 - 14k^2 - 8)$
First simplify inside the second group: $-3k^2 - 14k^2 = -17k^2$. So it becomes $(k^3 - 17k^2 - 8)$.
Now add everything: $-4k^2 + 4 + k^3 - 17k^2 - 8$.
Combine $k^2$ terms: $-4k^2 - 17k^2 = -21k^2$.
Combine constants: $4 - 8 = -4$.
Answer: $k^3 - 21k^2 - 4$

10) $(3 - 6a^2 - 8a^3) - (-6a^3 - 3a - 8a^2)$
Distribute the negative sign: $3 - 6a^2 - 8a^3 + 6a^3 + 3a + 8a^2$.
Combine $a^3$: $-8a^3 + 6a^3 = -2a^3$.
Combine $a^2$: $-6a^2 + 8a^2 = 2a^2$.
Combine $a$: $3a$.
Combine constants: $3$.
Answer: $-2a^3 + 2a^2 + 3a + 3$

11) $(12a^2 - 6a - 10b^2) - (10b - 2a^2 - 14a^2)$
Simplify inside the second group first: $-2a^2 - 14a^2 = -16a^2$. So it is $(10b - 16a^2)$.
Distribute the negative sign: $12a^2 - 6a - 10b^2 - 10b + 16a^2$.
Combine $a^2$: $12a^2 + 16a^2 = 28a^2$.
Answer: $28a^2 - 6a - 10b^2 - 10b$

12) $(9a - 5b^2 + 10c^3) - (13a^2 + 15c^3 - 7)$
Distribute the negative sign: $9a - 5b^2 + 10c^3 - 13a^2 - 15c^3 + 7$.
Combine $c^3$: $10c^3 - 15c^3 = -5c^3$.
Answer: $-13a^2 + 9a - 5b^2 - 5c^3 + 7$

13) $(c^4 + 12c^3 + 6c^2) + (6c^4 + 5c^3 + 7c^2)$
Combine $c^4$: $1 + 6 = 7c^4$.
Combine $c^3$: $12 + 5 = 17c^3$.
Combine $c^2$: $6 + 7 = 13c^2$.
Answer: $7c^4 + 17c^3 + 13c^2$

14) $(9t^3 + 5t^2 + 11n) + (-2t^3 + 9n - 8t^2)$
Combine $t^3$: $9 - 2 = 7t^3$.
Combine $t^2$: $5 - 8 = -3t^2$.
Combine $n$: $11 + 9 = 20n$.
Answer: $7t^3 - 3t^2 + 20n$

15) $(13a^2 + 11a - 2a^3) + (13a^2 - 3a - 6a^3)$
Combine $a^3$: $-2 - 6 = -8a^3$.
Combine $a^2$: $13 + 13 = 26a^2$.
Combine $a$: $11 - 3 = 8a$.
Answer: $-8a^3 + 26a^2 + 8a$

16) $(s^2 + 5s^4 + 12s) + (10s^3 + 7s + 5s^3)$
Simplify second group: $10s^3 + 5s^3 = 15s^3$.
Combine all: $5s^4 + 15s^3 + s^2 + (12s + 7s)$.
Answer: $5s^4 + 15s^3 + s^2 + 19s$

17) $(7 - 13x^2 - 11a) - (12x^2 + 8 - 4x^3)$
Distribute the negative sign: $7 - 13x^2 - 11a - 12x^2 - 8 + 4x^3$.
Combine $x^3$: $4x^3$.
Combine $x^2$: $-13 - 12 = -25x^2$.
Combine $a$: $-11a$.
Combine constants: $7 - 8 = -1$.
Answer: $4x^3 - 25x^2 - 11a - 1$

18) $(13a^2 - 6a^3 - 2a) - (13b^2 - 11a^2 + 9a)$
Distribute the negative sign: $13a^2 - 6a^3 - 2a - 13b^2 + 11a^2 - 9a$.
Combine $a^3$: $-6a^3$.
Combine $a^2$: $13 + 11 = 24a^2$.
Combine $a$: $-2 - 9 = -11a$.
Combine $b^2$: $-13b^2$.
Answer: $-6a^3 + 24a^2 - 11a - 13b^2$