Question

Разложите на множители
1)X^2y^2-z^2
2)a^2b^2-16
3)9-m^2n^2
4)b^2c^2-1
5)y^4-x^2
6)y^6-9
7)x^10-25
8)9-b^4

Answer 1

1) x²y² - z² = (xy)²  - z² = (xy - z)(xy +z)
2) a²b² - 16 = (ab)² - 4² = (ab - 4)(ab +4)
3) 9 - m²n²  =  - ((mn)²   - 3²) = -(mn - 3)(mn + 3)
4) b²c² - 1  = (bc)² - 1² = (bc -1)(bc+1)
5) y⁴ - x² = (y²)²  - x² = (y²  -x)(y²  +x)
6) y⁶  - 9  = (y³)²  - 3² = (y³  - 3)(y³ + 3)
7) x¹⁰ - 25 = (x⁵)²  - 5² = (x⁵ - 5)(x⁵ +5)
8) 9 - b⁴ = - ( (b²)²  - 3²) = - (b² - 3)(b² + 3)