Question

Разложить на множители:

1) 81-64x^2y^2=
2) (2a+7b)^2-(3а-5b)^2=
3) a^2n-1=
4) (1-5х)(1+5х)-(3х-1)^2=
5) (2b+a)(a-2b)+(a+3b)^2 =
6) 1/2a^2+ab+1/2b^2 =
7) y^4-8y^2+16 =
8) -c+c^7=

Answer 1

1) 81-64x^2y^2=(9-8xy)(9+8xy)
2) (2a+7b)^2-(3а-5b)^2=(2a+7b-3a+5b)(2a+7b+3a-5b)=(12b-a)(2b+5a)
3) a^2n-1= (a^n -1)(a^n +1)
4) (1-5х)(1+5х)-(3х-1)^2= 1-25x²-9x²+6x-1=6x-34x²=2x(3-17x)
5) (2b+a)(a-2b)+(a+3b)^2 =a²-4b²+a²+6ab+9b²=2a²+6ab+5b²
6) 1/2a^2+ab+1/2b^2 =1/2(a+b)²
7) y^4-8y^2+16 =(y²-4)²
8) -c+c^7=-c(1-c^6)=-c(1-c³)(1+c³)=-c(1-c)(1+c+c³)(1+c)(1-c+c³)