Представьте многочлен в виде произведения. 1) m3 - n3 + 2n - 2m 3) x6 + y6 + x2 + y2 5) x4 + xy3 - x3y - y4

1) m³-n³+2n-2m = (m³-n³) - 2 (n-m) = (n-m) (n²+mn+m²) - 2 (n-m) = (n-m) (n²+nm+m²-2)

3) x^6+y^6+x²+y² = (x²) ³ + (y²) ³ + (x²+y²) = ((x²+y²) (x^4-x²y²+y^4) + (x²+y²) = (x²+y²) (x^4-

-x²y²+y^4+1)

5) x^4+xy³-x³y-y^4 = (x^4-y^4) - (x³y-xy³) = (x²-y²) (x²+y²) - xy (x²-y²) = (x²-y²) (x²+y²-xy)

1) m³ - n³ + 2n - 2m = (m³ - n³) + 2 (n - m) = (m - n) (m² + mn + n²) - 2 (m - n) =

= (m - n) (m² + mn + n² - 2)

2) x⁶ + y⁶ + x² + y² = (x²) ³ + (y²) ³ + (x² + y²) = (x² + y²) (x⁴ - x²y² + y⁴) + (x² + y²) =

= (x² + y²) (x⁴ - x²y² + y⁴ + 1)

3) x⁴ + xy3 - x3y - y⁴ = x⁴ + 3xy - 3xy - y⁴ = x⁴ - y⁴ = (x²) ² - (y²) ² = (x² - y²) (x² + y²).