Please check and see if my answer are correct

1). 24v^2w^5x^8-20v^7w^9= -4v^2w^5(5v^5w^4-6x^8)

2). 81-25z^2= (5z+9)(9-5z)

3). 5y^3-7y^2-15y+21=(y^2-3)(5y-7)

4). x^2+4x-12= (x+6)(x-2)

5). 3x^2-26x+16= (x-8)(3x-2)

6).4v^6+6v^5-18v^4= 2v^4(2v-3)(v+3)

7). solve for y
y^2+6y+8=0 y= -2,-4

8).2v^2+4v-14=(v+1)^2= v=3,-5

Please check these for me

all correct.

Though I'd have written #2 as (9+5z)(9-5z) to associate it more readily with the difference of two squares.

1. Incorrect. The correct factorization would be:

24v^2w^5x^8 - 20v^7w^9 = 4v^2w^5(6x^8 - 5v^5w^4)

2. Correct.
81 - 25z^2 = (9 + 5z)(9 - 5z)

3. Correct.
5y^3 - 7y^2 - 15y + 21 = (y - 3)(5y^2 + 14y - 7)

4. Correct.
x^2 + 4x - 12 = (x + 6)(x - 2)

5. Correct.
3x^2 - 26x + 16 = (x - 8)(3x - 2)

6. Incorrect. The correct factorization would be:
4v^6 + 6v^5 - 18v^4 = 2v^4(2v^2 + 3v - 9)

7. Correct.
Solving the quadratic equation y^2 + 6y + 8 = 0 yields y = -2, -4.

8. Incorrect. The correct solution would be:
2v^2 + 4v - 14 = (v - 3)(v + 5)

Please note the corrected answers for question 1, 6, and 8.

To check if your answers are correct, we can expand the expressions on both sides of the given equations and compare them. Let's go through each question one by one:

1) 24v^2w^5x^8 - 20v^7w^9 = -4v^2w^5(5v^5w^4 - 6x^8)

To verify this equation, we can expand the right-hand side:
-4v^2w^5(5v^5w^4 - 6x^8) = -20v^7w^9 + 24v^2w^5x^8

The right-hand side of the equation is the same as the left-hand side, so your answer is correct.

2) 81 - 25z^2 = (5z + 9)(9 - 5z)

To verify this equation, we can expand the right-hand side:
(5z + 9)(9 - 5z) = 45z - 25z^2 + 81 - 45z

Simplifying the right-hand side gives us: 81 - 25z^2. This is the same as the left-hand side, so your answer is correct.

3) 5y^3 - 7y^2 - 15y + 21 = (y^2 - 3)(5y - 7)

Expanding the right-hand side:
(y^2 - 3)(5y - 7) = 5y^3 - 7y^2 - 15y + 21

The expanded right-hand side matches the left-hand side, so your answer is correct.

4) x^2 + 4x - 12 = (x + 6)(x - 2)

Expanding the right-hand side:
(x + 6)(x - 2) = x^2 - 2x + 6x - 12 = x^2 + 4x - 12

The expanded right-hand side matches the left-hand side, so your answer is correct.

5) 3x^2 - 26x + 16 = (x - 8)(3x - 2)

Expanding the right-hand side:
(x - 8)(3x - 2) = 3x^2 - 2x - 24x + 16 = 3x^2 - 26x + 16

The expanded right-hand side matches the left-hand side, so your answer is correct.

6) 4v^6 + 6v^5 - 18v^4 = 2v^4(2v - 3)(v + 3)

Expanding the right-hand side:
2v^4(2v - 3)(v + 3) = 2v^4(2v^2 + 6v - 3v - 9) = 4v^6 + 12v^5 - 6v^5 - 18v^4

The expanded right-hand side matches the left-hand side, so your answer is correct.

7) Solving for y: y^2 + 6y + 8 = 0

To solve this quadratic equation, we can factor it. The factors of 8 that add up to 6 are 2 and 4. So, we can rewrite the equation as:
(y + 2)(y + 4) = 0

Setting each factor equal to zero, we get:
y + 2 = 0 --> y = -2
y + 4 = 0 --> y = -4

The solutions for y are -2 and -4, which matches your answer.

8) Solving for v: 2v^2 + 4v - 14 = (v + 1)^2

Expanding the right-hand side:
(v + 1)^2 = v^2 + 2v + 1

So, the equation becomes:
2v^2 + 4v - 14 = v^2 + 2v + 1

Simplifying, we have:
v^2 + 2v - 15 = 0

To factor this quadratic equation, we need to find two numbers that multiply to -15 and add up to 2. The numbers are 5 and -3. Rewriting the equation, we get:
(v + 5)(v - 3) = 0

Setting each factor equal to zero, we have:
v + 5 = 0 --> v = -5
v - 3 = 0 --> v = 3

The solutions for v are -5 and 3, which matches your answer.

Overall, your answers are correct for all the given equations. Well done!