Question

pre - algebra
assignment
simplify each expression.

1. $(7a^{4}-6)-(3 + 7a)$
2. $(4p + 5)-(8p^{4}-6p)$
3. $(3m + m^{4})+(7m - 2m^{4})$
4. $(2x - 1)-(5x - 1)$
5. $(1 - 5n^{3})-(6n^{3}-8)$
6. $(2n^{2}-2n)-(n^{2}-6n)$
7. $(x^{2}-7x)+(3x - 8x^{2})$
8. $(6x + 6)+(6 + 7x)$
9. $(5x + 4x^{3})+(4x + 7x^{3})$
10. $(8x^{3}+5x)-(4x + 8x^{3})$
11. $(4b^{4}+3)+(4 + 4b^{4})$
12. $(x + 8)+(5x - 6)$
13. $(4v + v^{4})+(v - 7v^{4})$
14. $(2 + 8v^{4})-(4v^{4}-4)$
15. $(3 + 4x^{4})+(5x^{4}-5)$
16. $(x^{2}-6x^{4})-(3x^{2}+x^{4})$
17. $(4p + 3)-(6 - 7p)$
18. $(3x^{3}-x^{4})+(3x^{4}-5x^{3})$
19. $(4n^{2}+7)-(6 + 8n^{2})$
20. $(7 + 5k)+(3 + 5k)$

Explanation:

Let's solve each expression one by one:

1) \((7a^4 - 6) - (3 + 7a)\)

Step 1: Distribute the negative sign

\(7a^4 - 6 - 3 - 7a\)

Step 2: Combine like terms

\(7a^4 - 7a + (-6 - 3)\)
\(7a^4 - 7a - 9\)

Step 1: Distribute the negative sign

\(4p + 5 - 8p^4 + 6p\)

Step 2: Combine like terms

\(-8p^4 + (4p + 6p) + 5\)
\(-8p^4 + 10p + 5\)

Step 1: Remove parentheses

\(3m + m^4 + 7m - 2m^4\)

Step 2: Combine like terms

\((m^4 - 2m^4) + (3m + 7m)\)
\(-m^4 + 10m\)

Answer:

\(7a^4 - 7a - 9\)

2) \((4p + 5) - (8p^4 - 6p)\)