1)5a^2-5-4(a-1)^2 = 2)2(x+y)^2+x^2-y^2 = 3)a^4+ab^3-a^b-b^4= - вопрос №152541222222343444222252832430 от Milkyway3000 20.08.2022 15:27

Question

Алгебра: 1)5a^2-5-4(a-1)^2 = 2)2(x+y)^2+x^2-y^2 = 3)a^4+ab^3-a^b-b^4= 4)(x-y+4)^2-x^2+2xy-y^2= 5)x^3+y^3+2xy(x+y)= 6)49(y-4)^2-9(y+2)^2= решите ! !

Milkyway3000 · Answer

1)5a²-5-4(a-1)² =5(a²-1)-4(a-1)²=5(a-1)(a+1)-4(a-1)²=(a-1)(5a+5-4a+4)=(a-1)(a+9) 2)2(x+y)²+x²-y²=2(x+y)² - (x+y)(x-y)=(x+y)(2x+2y-x+y)=(x+y)(x+3y)
3)a⁴+ab³-a³b-b⁴=a⁴-b⁴+ab(b²-a²)=(a²-b²)(a²+b²)-ab(b²-a²)=(b²-a²)(a²+b²-ab)=(b-a)(a³+b³)
4)(x-y+4)²-x²+2xy-y²=(х-у+4)² -(х-у)²=(х-у+4-х+у)(х-у+4+х-у)=4(2х-2у+4)=8(х-у+2)
5)x³+y³+2xy(x+y)=(х+у)(х²-ху+у²)+2ху(х+у)=(х+у)(х²-ху+у²+2ху)=(х+у)(х²+ху+у²)
6)49(y-4)²-9(y+2)²==(7(у-4))²-(3(у+2))²=(7(у-4)-3(у+2))·(7(у-4)+3(у+2))=(7у-28-3у-6)97у-28+3у+6)= =(4у-34)·(10у-22)