Question

1. $(-4k^{4}+14 + 3k^{2})+(-3k^{4}-14k^{2}-8)$
2. $(3 - 6n^{5}-8n^{4})-(-6n^{4}-3n - 8n^{3})$
3. $(12a^{5}-6a - 10a^{3})-(10a - 2a^{5}-14a^{4})$
4. $(8n - 3n^{4}+10n^{2})-(3n^{2}+11n^{4}-7)$
5. $(-x^{4}+13x^{5}+6x^{3})+(6x^{3}+5x^{5}+7x^{4})$
6. $(9r^{3}+5r^{2}+11r)+(-2r^{3}+9r - 8r^{2})$
7. $(13n^{2}+11n - 2n^{4})+(-13n^{2}-3n - 6n^{4})$
8. $(-7x^{5}+14 - 2x)+(10x^{4}+7x + 5x^{5})$

Explanation:

Let's solve each problem one by one:

Problem 9: $(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8)$

Step 1: Combine like terms for $k^4$

$-4k^4 - 3k^4 = (-4 - 3)k^4 = -7k^4$

Step 2: Combine like terms for $k^2$

$3k^2 - 14k^2 = (3 - 14)k^2 = -11k^2$

Step 3: Combine constant terms

$14 - 8 = 6$

Step 4: Combine all terms

$-7k^4 - 11k^2 + 6$

Problem 10: $(3 - 6n^5 - 8n^4) - (-6n^4 - 3n - 8n^3)$

Step 1: Distribute the negative sign

$3 - 6n^5 - 8n^4 + 6n^4 + 3n + 8n^3$

Step 2: Combine like terms for $n^4$

$-8n^4 + 6n^4 = (-8 + 6)n^4 = -2n^4$

Step 3: Combine all terms

$-6n^5 + 8n^3 - 2n^4 + 3n + 3$ (rearranged in descending order of exponents)
$-6n^5 - 2n^4 + 8n^3 + 3n + 3$

Problem 11: $(12a^5 - 6a - 10a^3) - (10a - 2a^5 - 14a^4)$

Step 1: Distribute the negative sign

$12a^5 - 6a - 10a^3 - 10a + 2a^5 + 14a^4$

Step 2: Combine like terms for $a^5$

$12a^5 + 2a^5 = 14a^5$

Step 3: Combine like terms for $a$

$-6a - 10a = -16a$

Step 4: Combine all terms

$14a^5 + 14a^4 - 10a^3 - 16a$ (rearranged in descending order of exponents)

Problem 12: $(8n - 3n^4 + 10n^2) - (3n^2 + 11n^4 - 7)$

Step 1: Distribute the negative sign

$8n - 3n^4 + 10n^2 - 3n^2 - 11n^4 + 7$

Step 2: Combine like terms for $n^4$

$-3n^4 - 11n^4 = -14n^4$

Step 3: Combine like terms for $n^2$

$10n^2 - 3n^2 = 7n^2$

Step 4: Combine all terms

$-14n^4 + 7n^2 + 8n + 7$ (rearranged in descending order of exponents)

Problem 13: $(-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4)$

Step 1: Combine like terms for $x^5$

$13x^5 + 5x^5 = 18x^5$

Step 2: Combine like terms for $x^4$

$-x^4 + 7x^4 = 6x^4$

Step 3: Combine like terms for $x^3$

$6x^3 + 6x^3 = 12x^3$

Step 4: Combine all terms

$18x^5 + 6x^4 + 12x^3$ (rearranged in descending order of exponents)

Problem 14: $(9r^3 + 5r^2 + 11r) + (-2r^3 + 9r - 8r^2)$

Step 1: Combine like terms for $r^3$

$9r^3 - 2r^3 = 7r^3$

Step 2: Combine like terms for $r^2$

$5r^2 - 8r^2 = -3r^2$

Step 3: Combine like terms for $r$

$11r + 9r = 20r$

Step 4: Combine all terms

$7r^3 - 3r^2 + 20r$ (rearranged in descending order of exponents)

Problem 15: $(13n^2 + 11n - 2n^4) + (-13n^2 - 3n - 6n^4)$

Step 1: Combine like terms for $n^4$

$-2n^4 - 6n^4 = -8n^4$

Step 2: Combine like terms for $n^2$

$13n^2 - 13n^2 = 0$ (they cancel out)

Step 3: Combine like terms for $n$

$11n - 3n = 8n$

Step 4: Combine all terms

$-8n^4 + 8n$ (rearranged in descending order of exponents)

Problem 16: $(-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5)$

Step 1: Combine like terms for $x^5$

$-7x^5 + 5x^5 = -2x^5$

Step 2: Combine like terms for $x$

$-2x + 7x = 5x$

Step 3: Combine all terms

$-2x^5 + 10x^4 + 5x + 14$ (rearranged in descending order of exponents)

Final Answers:

1. $\boldsymbol{-7k^4 - 11k^2 + 6}$
2. $\boldsymbol{-6n^5 - 2n^4 + 8n^3 + 3n + 3}$
3. $\boldsymbol{14a^5 + 14a^4 - 10a^3 - 16a}$
4. $\boldsymbol{-14n^4 + 7n^2 + 8n + 7}$
5. $\boldsymbol{18x^5 + 6x^4 + 12x^3}$
6. $\boldsymbol{7r^3 - 3r^2 + 20r}$
7. $\boldsymbol{-8n^4 + 8n}$
8. $\boldsymbol{-2x^5 + 10x^4 + 5x + 14}$

Answer:

Let's solve each problem one by one:

Problem 9: $(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8)$

Step 1: Combine like terms for $k^4$

$-4k^4 - 3k^4 = (-4 - 3)k^4 = -7k^4$

Step 2: Combine like terms for $k^2$

$3k^2 - 14k^2 = (3 - 14)k^2 = -11k^2$

Step 3: Combine constant terms

$14 - 8 = 6$

Step 4: Combine all terms

$-7k^4 - 11k^2 + 6$

Problem 10: $(3 - 6n^5 - 8n^4) - (-6n^4 - 3n - 8n^3)$

Step 1: Distribute the negative sign

$3 - 6n^5 - 8n^4 + 6n^4 + 3n + 8n^3$

Step 2: Combine like terms for $n^4$

$-8n^4 + 6n^4 = (-8 + 6)n^4 = -2n^4$

Step 3: Combine all terms

$-6n^5 + 8n^3 - 2n^4 + 3n + 3$ (rearranged in descending order of exponents)
$-6n^5 - 2n^4 + 8n^3 + 3n + 3$

Problem 11: $(12a^5 - 6a - 10a^3) - (10a - 2a^5 - 14a^4)$

Step 1: Distribute the negative sign

$12a^5 - 6a - 10a^3 - 10a + 2a^5 + 14a^4$

Step 2: Combine like terms for $a^5$

$12a^5 + 2a^5 = 14a^5$

Step 3: Combine like terms for $a$

$-6a - 10a = -16a$

Step 4: Combine all terms

$14a^5 + 14a^4 - 10a^3 - 16a$ (rearranged in descending order of exponents)

Problem 12: $(8n - 3n^4 + 10n^2) - (3n^2 + 11n^4 - 7)$

Step 1: Distribute the negative sign

$8n - 3n^4 + 10n^2 - 3n^2 - 11n^4 + 7$

Step 2: Combine like terms for $n^4$

$-3n^4 - 11n^4 = -14n^4$

Step 3: Combine like terms for $n^2$

$10n^2 - 3n^2 = 7n^2$

Step 4: Combine all terms

$-14n^4 + 7n^2 + 8n + 7$ (rearranged in descending order of exponents)

Problem 13: $(-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4)$

Step 1: Combine like terms for $x^5$

$13x^5 + 5x^5 = 18x^5$

Step 2: Combine like terms for $x^4$

$-x^4 + 7x^4 = 6x^4$

Step 3: Combine like terms for $x^3$

$6x^3 + 6x^3 = 12x^3$

Step 4: Combine all terms

$18x^5 + 6x^4 + 12x^3$ (rearranged in descending order of exponents)

Problem 14: $(9r^3 + 5r^2 + 11r) + (-2r^3 + 9r - 8r^2)$

Step 1: Combine like terms for $r^3$

$9r^3 - 2r^3 = 7r^3$

Step 2: Combine like terms for $r^2$

$5r^2 - 8r^2 = -3r^2$

Step 3: Combine like terms for $r$

$11r + 9r = 20r$

Step 4: Combine all terms

$7r^3 - 3r^2 + 20r$ (rearranged in descending order of exponents)

Problem 15: $(13n^2 + 11n - 2n^4) + (-13n^2 - 3n - 6n^4)$

Step 1: Combine like terms for $n^4$

$-2n^4 - 6n^4 = -8n^4$

Step 2: Combine like terms for $n^2$

$13n^2 - 13n^2 = 0$ (they cancel out)

Step 3: Combine like terms for $n$

$11n - 3n = 8n$

Step 4: Combine all terms

$-8n^4 + 8n$ (rearranged in descending order of exponents)

Problem 16: $(-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5)$

Step 1: Combine like terms for $x^5$

$-7x^5 + 5x^5 = -2x^5$

Step 2: Combine like terms for $x$

$-2x + 7x = 5x$

Step 3: Combine all terms

$-2x^5 + 10x^4 + 5x + 14$ (rearranged in descending order of exponents)

Final Answers:

1. $\boldsymbol{-7k^4 - 11k^2 + 6}$
2. $\boldsymbol{-6n^5 - 2n^4 + 8n^3 + 3n + 3}$
3. $\boldsymbol{14a^5 + 14a^4 - 10a^3 - 16a}$
4. $\boldsymbol{-14n^4 + 7n^2 + 8n + 7}$
5. $\boldsymbol{18x^5 + 6x^4 + 12x^3}$
6. $\boldsymbol{7r^3 - 3r^2 + 20r}$
7. $\boldsymbol{-8n^4 + 8n}$
8. $\boldsymbol{-2x^5 + 10x^4 + 5x + 14}$