Question

9 $(-3m^4 + 3m) - (-7m^4 - 8m)$
10 $(19u^2 - 6u + 12) - (6u^2 - 6u + 7)$
11 $(h^3 - h) + (5h + 6) - (3h^2 + 4h - 9)$
12 $(5n - 3) + (2n^2 - 3n + 12)$
13 $(t^5 + 4t^3 - 2t) + (2t^3 + 6t - 4)$
14 $(4i^2 + 16i - 2) + (9i^2 - 2i + 7)$
15 $(16p^3 - p + 3) - (-3p^2 - p)$
16 $(c^3 - 2c + 1) - (2c^3 + c) + (4c^2 - 6c + 3)$
17 $(11k^2 + 2k) + (-2k^2 - 7k + 14)$
18 $(8w^4 - 3w + 4) - (-3w^4 + 2w^2 + 4w - 12)$

Explanation:

Problem 9

Step1: Distribute the negative sign

$(-3m^4 + 3m) + 7m^4 + 8m$

Step2: Combine like terms

$(-3m^4 + 7m^4) + (3m + 8m)$
$=4m^4 + 11m$

Problem 10

Step1: Distribute the negative sign

$19u^2 - 6u + 12 - 6u^2 + 6u - 7$

Step2: Combine like terms

$(19u^2 - 6u^2) + (-6u + 6u) + (12 - 7)$
$=13u^2 + 5$

Problem 11

Step1: Remove parentheses

$h^2 - h + 5h + 6 - 3h^2 - 4h + 9$

Step2: Combine like terms

$(h^2 - 3h^2) + (-h + 5h - 4h) + (6 + 9)$
$=-2h^2 + 15$

Problem 12

Step1: Remove parentheses

$5n - 3 + 2n^2 - 3n + 12$

Step2: Combine like terms

$2n^2 + (5n - 3n) + (-3 + 12)$
$=2n^2 + 2n + 9$

Problem 13

Step1: Remove parentheses

$t^5 + 4t^3 - 2t + 2t^3 + 6t - 4$

Step2: Combine like terms

$t^5 + (4t^3 + 2t^3) + (-2t + 6t) - 4$
$=t^5 + 6t^3 + 4t - 4$

Problem 14

Step1: Remove parentheses

$4i^2 + 16i - 2 + 9i^2 - 2i + 7$

Step2: Combine like terms

$(4i^2 + 9i^2) + (16i - 2i) + (-2 + 7)$
$=13i^2 + 14i + 5$

Problem 15

Step1: Distribute the negative sign

$16p^2 - p + 3 + 3p^2 + p$

Step2: Combine like terms

$(16p^2 + 3p^2) + (-p + p) + 3$
$=19p^2 + 3$

Problem 16

Step1: Distribute negative signs

$c^3 - 2c + 1 - 2c^3 - c + 4c^2 - 6c + 3$

Step2: Combine like terms

$(c^3 - 2c^3) + 4c^2 + (-2c - c - 6c) + (1 + 3)$
$=-c^3 + 4c^2 - 9c + 4$

Problem 17

Step1: Remove parentheses

$11k^2 + 2k - 2k^2 - 7k + 14$

Step2: Combine like terms

$(11k^2 - 2k^2) + (2k - 7k) + 14$
$=9k^2 - 5k + 14$

Problem 18

Step1: Distribute the negative sign

$8w^4 - 3w + 4 + 3w^4 - 2w^2 - 4w + 12$

Step2: Combine like terms

$(8w^4 + 3w^4) - 2w^2 + (-3w - 4w) + (4 + 12)$
$=11w^4 - 2w^2 - 7w + 16$

Answer:

1. $4m^4 + 11m$
2. $13u^2 + 5$
3. $-2h^2 + 15$
4. $2n^2 + 2n + 9$
5. $t^5 + 6t^3 + 4t - 4$
6. $13i^2 + 14i + 5$
7. $19p^2 + 3$
8. $-c^3 + 4c^2 - 9c + 4$
9. $9k^2 - 5k + 14$
10. $11w^4 - 2w^2 - 7w + 16$