1)
х²(х+4) – 20х(х+4) + 100(х+4) =
= (х+4)(х² – 20х + 100) =
= (х+4)(х – 10)²
2)
а² – 36 – 2а(36 – а²) – а²(36 – а²) =
= (а² – 36) + 2а(а² – 36) + а²(а² – 36) =
= (а² – 36)(1 + 2а + а²) =
= (а² – 36)(1+а)²
3)
а²(b-1) –
b²(a-1) =
= a²b – a² –
ab² + b² =
= (a²b – ab²) -
(a² – b²) =
= ab(a – b)
– (a – b)(a+b) =
= (a – b)(ab
– a – b)
4)
(m-n)(n³-p³)
– (n-p)(m³ – n³) =
= (m - n)(n
- p)(n²+ np + p²) – (n-p)(m – n)(m² + mn + n²) =
= (m - n)(n
- p)((n²+ np + p²) –(m² + mn + n²)) =
= (m - n)(n
- p)((n²+ np + p² –m² - mn - n²)