Question

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

Explanation:

Let's solve each problem one by one:

Problem 31:

Step1: Remove parentheses

$(11b^{3}-3b^{4})-(3b^{3}-11b^{4}+7b)=11b^{3}-3b^{4}-3b^{3}+11b^{4}-7b$

Step2: Combine like terms

For $b^{4}$: $-3b^{4}+11b^{4}=8b^{4}$
For $b^{3}$: $11b^{3}-3b^{3}=8b^{3}$
The term with $b$: $-7b$
So the result is $8b^{4}+8b^{3}-7b$

Step1: Remove parentheses

$(12p + 14p^{5})+(8-14p^{5}-4p)=12p + 14p^{5}+8-14p^{5}-4p$

Step2: Combine like terms

For $p^{5}$: $14p^{5}-14p^{5}=0$
For $p$: $12p-4p = 8p$
The constant term: $8$
So the result is $8p + 8$

Step1: Remove parentheses

$(14p^{5}+4p^{3})-(4p^{4}-14p^{3}+14p^{5})=14p^{5}+4p^{3}-4p^{4}+14p^{3}-14p^{5}$

Step2: Combine like terms

For $p^{5}$: $14p^{5}-14p^{5}=0$
For $p^{3}$: $4p^{3}+14p^{3}=18p^{3}$
The term with $p^{4}$: $-4p^{4}$
So the result is $-4p^{4}+18p^{3}$

Answer:

$8b^{4}+8b^{3}-7b$

Problem 32: