Expand the following: [(a+b^2)(a-b^2)]^5 Show the complete solution to explain the answer.

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We have to expand [(a+b^2)(a-b^2)]^5

[(a+b^2)(a-b^2)]^5

use (a + b)(a - b) = (a^2 - b^2)

=> [a^2 - b^4]^5

use the binomial theorem (x - y)^5 = -y^5 + 5*x*y^4 - 10*x^2*y^3 + 10*x^3*y^2 - 5*x^4*y + x^5

=> a^10 - 5*a^8*b^4 + 10a^6*b^8 - 10*a^4*b^12 + 5*a^2*b^16 -...

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We have to expand [(a+b^2)(a-b^2)]^5

[(a+b^2)(a-b^2)]^5

use (a + b)(a - b) = (a^2 - b^2)

=> [a^2 - b^4]^5

use the binomial theorem (x - y)^5 = -y^5 + 5*x*y^4 - 10*x^2*y^3 + 10*x^3*y^2 - 5*x^4*y + x^5

=> a^10 - 5*a^8*b^4 + 10a^6*b^8 - 10*a^4*b^12 + 5*a^2*b^16 - b^20

The expansion of [(a+b^2)(a-b^2)]^5 is a^10 - 5*a^8*b^4 + 10a^6*b^8 - 10*a^4*b^12 + 5*a^2*b^16 - b^20

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