5.54. Разложите на множители. 1) (5а+6)²-81;
2) 25-(а+7)²;
3)9m²-(1+2)²;
4) (5x-3y)²-16x²;
5) (5c-3d)²-9d²;
6) 49m²-(n+8m)².​

1) (5а+6)^2-81 = (5а+6-9)•(5а+6+9) = (5а-3)•5(а+3) = 5(5а-3)•(а+3)

2)25-(а+7)^2 = (5-(а-7))•(5+(а+7)) = (5-а-7)•(5+а+7) = (-2-а)•(12+а)

3)9m^2-(1+2)^2 = (3m-(1+2))•(3m+(1+2)) = (3m-3)•(3m+3) = 3(m-1)•3(m+1) = 3•3(m-1)•(m+1) = 9•(m-1)•(m+1)

4) (5х-3у)^2-16х^2 = (5х-3у-4х)•(5х-3у+4х) = (х-3у)•(9х-3у) = (х-3у)•3(3х-у) = 3•(х-3у)•(3х-у)

5) (5с-3d)^2-9d^2 = (5с-3d-3d)•(5с-3d+3d) = (5с-6d)•5c = 5c•(5с-6d)

6)49m^2-(n+8m)^2 = (7m-(n+8m))•(7m+(n+8m)) = (7m-n-8m)•(7m+n+8m) = (-m-n)•(15m+n)