how to factor 625r^4-p^4

Question

how to factor 625r^4-p^4

Answer 1

Hi Nick,

 

25²(r²)² - (p²)²

Using the equation a²-b² = (a-b)(a+b)

[25(r²) - (p²)][25(r²) + (p²)]

Using the equation a2-b2 = (a-b)(a+b) again

5²r² - p² = (5r + p)(5r - P)

final result is (5r + p)(5r - P)(25r^r + p²)

Answer 2

625r⁴p⁴

5⁴r⁴p⁴

(5rp)⁴