Question

Разложите на множители: a) 100a^4-16b^2; б) 9x^2-(x-1)^2

Answer 1

a) 100$a^{4}$ - 16b² = (10a²-4b)(10a²+4b)
b) 9x²-(x-1)² = (3x-(x-1))(3x+(x-1))

Answer 2

100а⁴ - 16b² =  4*(25a⁴  - 4b²) = 4*( (5a²)²  - (2b)²) = 4*(5a² - 2b)(5a² + 2b)

9x² - (x-1)²  = (3x)²  - (x-1)² = (3x  - (x-1))(3x + (x-1) ) = 
= (3x  - x + 1)(3x  + x  - 1) = (2x + 1)(4x - 1)