Question

DAU COROANĂ!!! Rezolvați după model!​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x⁴ - 625 = (x²)² - 25² = (x²-25)(x²+25) = (x-5)(x+5)(x²+25)

b) 9x² - 100 = (3x)² - 10² = (3x-10)(3x+10)

c) y² - 16a² = y² - (4a)² = (y-4a)(y+4a)

d) a² - 1/9 = a² - (1/3)² = (a -1/3)(a +1/3)

e) 25a² - 16x² = (5a)² - (4x)² = (5a-4x)(5a+4x)

f) x² - 2 = x² - (√2)² = (x-√2)(x+√2)

g) x² - 5 = x² - (√5)² = (x-√5)(x+√5)

h) x⁴ - 1 = (x²)² - 1² = (x²-1)(x²+1) = (x-1)(x+1)(x²+1)

i) x⁴ - 81 = (x²)² - 9² = (x²-9)(x²+9) = (x-3)(x+3)(x²+9)

j) 16x⁴ - 1 = 2⁴x⁴ - 1 = (2²x²)² - 1² = (4x²)² - 1² =

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