$$ \begin{array}{lll} ext { (g) } x^{2}-2 x y+x y-2 y^{2} & ext { (h) } 7 x^{3}-21 x+2 x^{2} y-6 y & ext { (i) } 4 a y^{2}-8 a+12 b y^{2}-24 b \ ext { (j) } p^{3}-2 p q^{2}+4 p^{2} q-8 q^{3} & ext { (k) } 2 m^{3}-4 m n+6 m^{2} n-12 n^{2} & ext { (l) } a x-b x-a+b \ ext { (m) } a x-4 x-a+4 & ext { (n) } a x+b x-a-b & ext { (o) } a x-b x-3 a+3 b \ ext { (p) } a x-2 b x-4 a+8 b & ext { (q) } 2 a x+3 b x-8 a-12 b & ext { (r) } a x-b x-3 a+3 b \ ext { (s) } 3 m x-9 m y-2 n x+6 n y & ext { (t) } 10 a x-15 b x-4 a y+6 b y & ext { (u) } x^{3}-2 x-x^{2}+2 \ ext { (v) } x^{3}-3 x-x^{2}+3 & ext { (w) } x^{3}-5 x-2 x^{2}+10 & ext { (x) } a^{3}+3 a b^{2}-3 a^{2} b-9 b^{3}\end{array} $$

Question

$$ \begin{array}{lll}	ext { (g) } x^{2}-2 x y+x y-2 y^{2} & 	ext { (h) } 7 x^{3}-21 x+2 x^{2} y-6 y & 	ext { (i) } 4 a y^{2}-8 a+12 b y^{2}-24 b \ 	ext { (j) } p^{3}-2 p q^{2}+4 p^{2} q-8 q^{3} & 	ext { (k) } 2 m^{3}-4 m n+6 m^{2} n-12 n^{2} & 	ext { (l) } a x-b x-a+b \ 	ext { (m) } a x-4 x-a+4 & 	ext { (n) } a x+b x-a-b & 	ext { (o) } a x-b x-3 a+3 b \ 	ext { (p) } a x-2 b x-4 a+8 b & 	ext { (q) } 2 a x+3 b x-8 a-12 b & 	ext { (r) } a x-b x-3 a+3 b \ 	ext { (s) } 3 m x-9 m y-2 n x+6 n y & 	ext { (t) } 10 a x-15 b x-4 a y+6 b y & 	ext { (u) } x^{3}-2 x-x^{2}+2 \ 	ext { (v) } x^{3}-3 x-x^{2}+3 & 	ext { (w) } x^{3}-5 x-2 x^{2}+10 & 	ext { (x) } a^{3}+3 a b^{2}-3 a^{2} b-9 b^{3}\end{array} $$

UpStudy AI · Accepted Answer

Let's simplify each of the given expressions step by step. I will provide the content for each expression first and then call the appropriate tool to simplify them.

1. **(g)** $$ x^{2}-2 x y+x y-2 y^{2} $$
2. **(h)** $$ 7 x^{3}-21 x+2 x^{2} y-6 y $$
3. **(i)** $$ 4 a y^{2}-8 a+12 b y^{2}-24 b $$
4. **(j)** $$ p^{3}-2 p q^{2}+4 p^{2} q-8 q^{3} $$
5. **(k)** $$ 2 m^{3}-4 m n+6 m^{2} n-12 n^{2} $$
6. **(l)** $$ a x-b x-a+b $$
7. **(m)** $$ a x-4 x-a+4 $$
8. **(n)** $$ a x+b x-a-b $$
9. **(o)** $$ a x-b x-3 a+3 b $$
10. **(p)** $$ a x-2 b x-4 a+8 b $$
11. **(q)** $$ 2 a x+3 b x-8 a-12 b $$
12. **(r)** $$ a x-b x-3 a+3 b $$
13. **(s)** $$ 3 m x-9 m y-2 n x+6 n y $$
14. **(t)** $$ 10 a x-15 b x-4 a y+6 b y $$
15. **(u)** $$ x^{3}-2 x-x^{2}+2 $$
16. **(v)** $$ x^{3}-3 x-x^{2}+3 $$
17. **(w)** $$ x^{3}-5 x-2 x^{2}+10 $$
18. **(x)** $$ a^{3}+3 a b^{2}-3 a^{2} b-9 b^{3} $$

Now, I will call the tool to simplify all these expressions in parallel.
Simplify the expression by following steps:
- step0: Solution:
  $$4ay^{2}-8a+12by^{2}-24b$$
Calculate or simplify the expression $$ a^{3}+3 a b^{2}-3 a^{2} b-9 b^{3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$a^{3}+3ab^{2}-3a^{2}b-9b^{3}$$
Calculate or simplify the expression $$ a x-2 b x-4 a+8 b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax-2bx-4a+8b$$
Calculate or simplify the expression $$ 10 a x-15 b x-4 a y+6 b y $$.
Simplify the expression by following steps:
- step0: Solution:
  $$10ax-15bx-4ay+6by$$
Calculate or simplify the expression $$ 2 a x+3 b x-8 a-12 b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$2ax+3bx-8a-12b$$
Calculate or simplify the expression $$ a x-b x-3 a+3 b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax-bx-3a+3b$$
Calculate or simplify the expression $$ 3 m x-9 m y-2 n x+6 n y $$.
Simplify the expression by following steps:
- step0: Solution:
  $$3mx-9my-2nx+6ny$$
Calculate or simplify the expression $$ a x-b x-a+b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax-bx-a+b$$
Calculate or simplify the expression $$ p^{3}-2 p q^{2}+4 p^{2} q-8 q^{3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$p^{3}-2pq^{2}+4p^{2}q-8q^{3}$$
Calculate or simplify the expression $$ 2 m^{3}-4 m n+6 m^{2} n-12 n^{2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$2m^{3}-4mn+6m^{2}n-12n^{2}$$
Calculate or simplify the expression $$ x^{3}-3 x-x^{2}+3 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x^{3}-3x-x^{2}+3$$
Calculate or simplify the expression $$ x^{3}-2 x-x^{2}+2 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x^{3}-2x-x^{2}+2$$
Calculate or simplify the expression $$ x^{2}-2 x y+x y-2 y^{2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x^{2}-2xy+xy-2y^{2}$$
- step1: Add the terms:
  $$x^{2}-xy-2y^{2}$$
Calculate or simplify the expression $$ 7 x^{3}-21 x+2 x^{2} y-6 y $$.
Simplify the expression by following steps:
- step0: Solution:
  $$7x^{3}-21x+2x^{2}y-6y$$
Calculate or simplify the expression $$ a x+b x-a-b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax+bx-a-b$$
Calculate or simplify the expression $$ a x-b x-3 a+3 b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax-bx-3a+3b$$
Calculate or simplify the expression $$ a x-4 x-a+4 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$ax-4x-a+4$$
Calculate or simplify the expression $$ x^{3}-5 x-2 x^{2}+10 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x^{3}-5x-2x^{2}+10$$
Here are the simplified results for each expression:

1. **(g)** $$ x^{2}-2 x y+x y-2 y^{2} $$ simplifies to $$ x^{2}-xy-2y^{2} $$
2. **(h)** $$ 7 x^{3}-21 x+2 x^{2} y-6 y $$ remains $$ 7x^{3}-21x+2x^{2}y-6y $$
3. **(i)** $$ 4 a y^{2}-8 a+12 b y^{2}-24 b $$ remains $$ 4ay^{2}-8a+12by^{2}-24b $$
4. **(j)** $$ p^{3}-2 p q^{2}+4 p^{2} q-8 q^{3} $$ remains $$ p^{3}-2pq^{2}+4p^{2}q-8q^{3} $$
5. **(k)** $$ 2 m^{3}-4 m n+6 m^{2} n-12 n^{2} $$ remains $$ 2m^{3}-4mn+6m^{2}n-12n^{2} $$
6. **(l)** $$ a x-b x-a+b $$ simplifies to $$ ax-bx-a+b $$
7. **(m)** $$ a x-4 x-a+4 $$ simplifies to $$ ax-4x-a+4 $$
8. **(n)** $$ a x+b x-a-b $$ simplifies to $$ ax+bx-a-b $$
9. **(o)** $$ a x-b x-3 a+3 b $$ simplifies to $$ ax-bx-3a+3b $$
10. **(p)** $$ a x-2 b x-4 a+8 b $$ simplifies to $$ ax-2bx-4a+8b $$
11. **(q)** $$ 2 a x+3 b x-8 a-12 b $$ simplifies to $$ 2ax+3bx-8a-12b $$
12. **(r)** $$ a x-b x-3 a+3 b $$ simplifies to $$ ax-bx-3a+3b $$
13. **(s)** $$ 3 m x-9 m y-2 n x+6 n y $$ simplifies to $$ 3mx-9my-2nx+6ny $$
14. **(t)** $$ 10 a x-15 b x-4 a y+6 b y $$ simplifies to $$ 10ax-15bx-4ay+6by $$
15. **(u)** $$ x^{3}-2 x-x^{2}+2 $$ simplifies to $$ x^{3}-2x-x^{2}+2 $$
16. **(v)** $$ x^{3}-3 x-x^{2}+3 $$ simplifies to $$ x^{3}-3x-x^{2}+3 $$
17. **(w)** $$ x^{3}-5 x-2 x^{2}+10 $$ simplifies to $$ x^{3}-5x-2x^{2}+10 $$
18. **(x)** $$ a^{3}+3 a b^{2}-3 a^{2} b-9 b^{3} $$ simplifies to $$ a^{3}+3ab^{2}-3a^{2}b-9b^{3} $$

If you need further assistance or additional simplifications, feel free to ask!
Here are the simplified forms of the given expressions: 1. **(g)** $$ x^{2} - xy - 2y^{2} $$ 2. **(h)** $$ 7x^{3} - 21x + 2x^{2}y - 6y $$ 3. **(i)** $$ 4ay^{2} - 8a + 12by^{2} - 24b $$ 4. **(j)** $$ p^{3} - 2pq^{2} + 4p^{2}q - 8q^{3} $$ 5. **(k)** $$ 2m^{3} - 4mn + 6m^{2}n - 12n^{2} $$ 6. **(l)** $$ ax - bx - a + b $$ 7. **(m)** $$ ax - 4x - a + 4 $$ 8. **(n)** $$ ax + bx - a - b $$ 9. **(o)** $$ ax - bx - 3a + 3b $$ 10. **(p)** $$ ax - 2bx - 4a + 8b $$ 11. **(q)** $$ 2ax + 3bx - 8a - 12b $$ 12. **(r)** $$ ax - bx - 3a + 3b $$ 13. **(s)** $$ 3mx - 9my - 2nx + 6ny $$ 14. **(t)** $$ 10ax - 15bx - 4ay + 6by $$ 15. **(u)** $$ x^{3} - 2x - x^{2} + 2 $$ 16. **(v)** $$ x^{3} - 3x - x^{2} + 3 $$ 17. **(w)** $$ x^{3} - 5x - 2x^{2} + 10 $$ 18. **(x)** $$ a^{3} + 3ab^{2} - 3a^{2}b - 9b^{3} $$ If you need further assistance or additional simplifications, feel free to ask!

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