Question: Solve the following algebraic expressions using the indicated operations. Make sure to show your solution. Write your answers in a 1 whole sheet of pad paper.
1. $(13x-13y+7z)+(x-24y+4z)+(-23x+17y-10z)$
2. $(9x^2-10xy+17y^2)+(-14y^2-10xy+8x^2)+(5xy+19y^2-7x^2)$
3. $(-14p^2+6p^3-3p^2+2p-10)+(5p^4-6p^2+4p^3-3p)+(3-2p+5p^2-7p^4+8p^5)$
4. $(\frac{3}{4}m^2+\frac{5}{6}mn-\frac{1}{3}n^2)+(\frac{1}{2}m^2+5mn-\frac{7}{12}n^2)+(\frac{1}{3}mn+n^2)$
5. $(x^5y^2z-7x^3y^3z^2+9x^2y^2z^4+7xy^4z^3)+(3xy^4z^3-21x^2y^2z^4+7x^5y^2z)+(2x^2y^2z^4+10x^3y^3z^2)$
6. $(-15z+9t-14y+7w-3x)-(8t-15w+23x-19y+2z)$
7. $(7p^2+14pq-3q^2)-(2p^2-7pq+9q^2)$
8. $(23s^3-2s^2+7s+29s^5+31)-(12s^5-19s^4+14s^3-2s)$
9. $2(a-b)+3(4a-3b)-(7a+b)-2(3a-2b)$
10. $2a-b+c-2[4a+2(b-3c)+4(a-2b+10)-c]+a-b$
11. $(4xy-2x+5y+4)(2x-3y)$
12. $(9x^4-3x^2+2x-3x^3-4)(3-2x+5x^2)$
13. $(a+2b+3c-4d)(a+2b-3c+4d)$
14. $(x-\frac{3}{4})(x+\frac{5}{7})$
15. $(m^{\frac{1}{2}}+3n^{\frac{1}{2}})^2$
16. $(x^3-4x^2+5x-3)\div(x+1)$
17. $(15x^3+41x^2+2x-28)\div(3x+7)$
18. $(x^3+y^3)\div(x+y)$
19. $\frac{12x^4-13x+5x^2-5+x^3}{3x^2-2x-1}$
20. $\frac{2x^3-11x^2y+13xy^2-7y^3}{x-4y}$
1. **Problem:** Simplify $(13x-13y+7z)+(x-24y+4z)+(-23x+17y-10z)$.
2. **Formula:** Combine like terms by adding coefficients of $x$, $y$, and $z$.
3. **Work:**
$$ (13x + x - 23x) + (-13y - 24y + 17y) + (7z + 4z - 10z) $$
$$ = (13 + 1 - 23)x + (-13 - 24 + 17)y + (7 + 4 - 10)z $$
$$ = (-9)x + (-20)y + 1z $$
4. **Answer:** $-9x - 20y + z$