Hi! I just want you to check if my answers are correct.

Factor the expressions:
1. 15a^2(b-2)^2 + 20a^3(b-2)^3 = my answer is 5a^2(b-2)^2 [3 + 4a(b-2)]
2. 18p^2q^3 (r-6)+ 24(r-6) = my answer is 6(r-6)[3p^2q^3 + 4]
3. 24(x-y)^2 + 48(y-x) - 72(x-y)^3 = my answer is 24[(x-y)^2 + 2(y-x) - 3(x-y)^3]
Lastly, -8.4x^3y^4 - 3.6x^2y^5 - 4.8x^4y^3. I don't have an answer for it yet.
Would appreciate your response. Thank you. :)

1. Good but you my want to distribute the parentheses inside the bracket.

2. Good
3. Hint: to out a negative sign in the middle term.

-8.4x^3y^4 - 3.6x^2y^5 - 4.8x^4y^3

Factor out -1.2x^2y^3 to get

-1.2x^2y^3(7xy + 3y^2 + 4x^2)
Rearrange terms to get

-1.2x^2y^3(4x^2 + 7xy + 3y^2)
Now factor that to get

-1.2x^2y^3(x+y)(4x+3y)

Sure! Let's check if your answers for the first three expressions are correct.

1. 15a^2(b-2)^2 + 20a^3(b-2)^3 = 5a^2(b-2)^2 [3 + 4a(b-2)]
To factor the expression, we can notice that there is a common factor, which is (b-2)^2. Factoring it out, we get:
15a^2(b-2)^2 + 20a^3(b-2)^3
= (b-2)^2 * (15a^2 + 20a^3(b-2))
= 5a^2(b-2)^2 * (3 + 4a(b-2))

Your answer, 5a^2(b-2)^2 [3 + 4a(b-2)], is correct. Well done!

2. 18p^2q^3(r-6) + 24(r-6) = 6(r-6)[3p^2q^3 + 4]
To factor this expression, we can notice that there is a common factor, which is (r-6). Factoring it out, we get:
18p^2q^3(r-6) + 24(r-6)
= 6(r-6)(3p^2q^3 + 4)

Your answer, 6(r-6)[3p^2q^3 + 4], is correct.

3. 24(x-y)^2 + 48(y-x) - 72(x-y)^3 = 24[(x-y)^2 + 2(y-x) - 3(x-y)^3]
To factor this expression, we can notice that there is a common factor, which is (x-y). Factoring it out, we get:
24(x-y)^2 + 48(y-x) - 72(x-y)^3
= 24[(x-y)^2 - 2(y-x) + 3(x-y)^3]

Your answer, 24[(x-y)^2 + 2(y-x) - 3(x-y)^3], is incorrect. The signs inside the brackets should be opposite since (x-y) = -(y-x). The correct answer is 24[(x-y)^2 - 2(y-x) + 3(x-y)^3].

Now, let's factor the last expression:

-8.4x^3y^4 - 3.6x^2y^5 - 4.8x^4y^3
To factor this expression, we can notice that there is a common factor, which is x^2y^3. Factoring it out, we get:
-8.4x^3y^4 - 3.6x^2y^5 - 4.8x^4y^3
= x^2y^3(-8.4xy - 3.6y^2 - 4.8x^2)

So the factored expression is x^2y^3(-8.4xy - 3.6y^2 - 4.8x^2).

I hope this helps! Let me know if you have any other questions.