Question

15d-15d^3 p^5-p^3 625b^3-b^5 500a^5-45a^3 Розкладіть множники

Answer 1

Объяснение:

15d-15d^3=15d(1-d^2)

p^5-p^3=p^3(p^2-1)

625b^3-b^5=b^3(625-b^2)

500a^5-45a^3=5a^3(10a-3)(10a+3)

Answer 2

To factor the given expression, let's group the terms and look for common factors in each group:

1. Group the terms with 'd': 15d - 15d^3 p^5

Factor out 'd' from both terms: d(15 - 15d^2 p^5)

2. Group the terms with 'p': p^3 - 625b^3

This is a difference of cubes, which can be factored as follows: (p - 5b)(p^2 + 5bp + 25b^2)

3. Group the terms with 'b': 500a^5 - 45a^3

Factor out '5a^3' from both terms: 5a^3(100a^2 - 9)

Now, the complete factored expression is:

d(15 - 15d^2 p^5) - (p - 5b)(p^2 + 5bp + 25b^2) - 5a^3(100a^2 - 9)

Please note that I'm assuming you meant to have subtraction signs (-) between the terms, as you wrote "15d-15d^3 p^5-p^3 625b^3-b^5 500a^5-45a^3." If that's not the case, and you meant something else, please clarify the expression and I'll be happy to help further!