1) (а+в)^2-(а-в)^2 = a^2 + 2ab +b^2 - a^2 + 2ab - b^2 = 4ab
2) (м+4)^2-4(м+1)^2 = m^2 + 8m + 16 - 4m^2 - 8m - 4 = -3m^2 + 12
3) 3(2-у)^2+4(у-5)^2 = 3(4-2y+y^2) + 4(y^2-10y+25) = 12-4y+3y^2+4y^2-40y+100 =
=7y^2-44y+112
4) 5(3-5х)^2-5(3х-7)(3х+7) = 5(9-30x +25x^2) - 5(9x^2 - 21x + 21x -49) = =45-150x+125^2-45x^2+245 = 80x^2-150x+290
5) (а+1)^2+3(а-1)^2-5(а-1)(а+1)= a^2+2a+1+3(a^2-2a+1)-5(a^2-a+a-1) = =a^2+2a+1+3a^2-6a+3-5a^2+5= -a^2-4a+9
6) (х-1)^2-4(х+1)^2-6(х+1)(х-1)= x^2-2x+1-4(x^2+2x+1)-6(x^2+x-x-1)= =x^2-2x+1-4x^2-8x-4-6x^2+6=-9x^2-10x+3
2.Выполните действия:
1) ((3а+в)^2-(а+3в)^2)*2ав=(9a^2+6ab+b^2-a^2-6ab-9b^2)*2ab = =(8a^2-8b^2)*2ab=16a^3b-16ab^3
2) ((х^2+2х)^2+(2х^2-х)^2)/5х^2
= (x^4+4x^3+4x^2+4x^4-4x^3+x^2)/5x^2 = = (5x^4+5x^2)/5x^2 = 5x^2(x^2+1)/5x^2= x^2+1