Question

(х^2 -7у^3 )^2 +(х^2 +7у^3)^ 2) (5а^3 - 4b)^2 + (4 b+ 5a ^3 )^2

Answer 1

1)  (х² -7у³)² +(х² +7у³)² =
  = х⁴ - 14х²у³ + 49у⁶ + х⁴ + 14х²у³ + 49у⁶ =
  = 2х⁴ + 98у⁶

2) (5a³ - 4b)² +(4b +5a³)² =
  = 25a⁶ - 40a³b + 16b² + 16b² + 40a³b + 25a⁶ =
  = 50a⁶ + 32b²

Answer 2

Let's simplify the expression step by step:

1. (х^2 - 7у^3)^2 = х^4 - 14х^2у^3 + 49у^6
2. (х^2 + 7у^3)^2 = х^4 + 14х^2у^3 + 49у^6

Now, we'll use these results to simplify the expression further:

(х^2 - 7у^3)^2 + (х^2 + 7у^3)^2 = (х^4 - 14х^2у^3 + 49у^6) + (х^4 + 14х^2у^3 + 49у^6)

Now, combine like terms:

= 2х^4 + 98y^6

Next, we'll simplify the second part of the expression:

(5а^3 - 4b)^2 = (5а^3 - 4b) * (5а^3 - 4b) = 25а^6 - 20а^3b - 20а^3b + 16b^2 = 25а^6 - 40а^3b + 16b^2

Similarly,

(4b + 5a^3)^2 = (4b + 5a^3) * (4b + 5a^3) = 16b^2 + 20a^3b + 20a^3b + 25a^6 = 25a^6 + 40a^3b + 16b^2

Now, combine the second part of the expression:

(5а^3 - 4b)^2 + (4 b+ 5a^3)^2 = (25а^6 - 40а^3b + 16b^2) + (25a^6 + 40a^3b + 16b^2)

Now, combine like terms:

= 50a^6 + 32b^2

So, the final simplified expression is:

2х^4 + 98y^6 + 50a^6 + 32b^2