Разложите на множители: 1) a3 + 8b3; 2) x2y - 36y3; 3) - 5m2 + 10mn - 5n2; 4) 4ab - 28b + 8a - 56; 5) a4 - 81.

1) a³+8b³ = (a+2b) (a²-2ab+4b²)

2) x²y-36y³=y (x²-36y²) = y (x-6y) (x+6y)

3) - 5m²+10mn-5n² / : (-5)

-5m²+10mn-5n²=m²-2mn+n² = (m-n) ²

4) 4ab-28b+8a-56 / : 4

4ab-28b+8a-56 = (ab-7b) + (2a-14) = b (a-7) + 2 (a-7) = (a-7) (b+2)

5) a⁴-81 = (a²) ² - (3²) ² = (a²-3²) (a²+3²) = (a²-9) (a²+9) = (a-3) (a+3) (a²+9)