Представить в виде произведения выражение:

1) x^2 (x+4) - 20x (x+4) + 100 (x+4)

2) a^2-36-2a (36-a^2) - a^2 (36-a^2)

3) a^2 (b-1) - b^2 (a-1)

4) (m-n) (n^3-p^3) - (n-p) (m^3-n^3)

1) x² (x+4) - 20x (x+4) + 100 (x+4) = (x+4) (x²-20x+100) = (x+4) (x-10) ²

2) a²-36-2a (36-a²) - a² (36-a²) = (36-a²) (-1-2a-a²) = (a²-36) (a²+2a+1) = (a²-36) (a+1) ²

3) a² (b-1) - b² (a-1) = a²b-a²-b²a+b²=ab (a-b) + (b²-a²) = - ab (b-a) + (b-a) (b+a) = (b-a) (-ab+b+a)

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) (np+p²-m²-mn) = (m-n) (n-p) (n (p-m) + (p-m) (p+m)) = (m-n) (n-p) (p-m) (n+p+m)