m11m

Verified answer

Вариант 1.
1.
а) (с-6)²=с²-12с+36
б) (2a-3b)²=4a²-12ab+9b²
в) (5-a)(5+a)=25-a²
г) (7x+10y)(10y-7x)=100y²-49x²
д) (3a-0.2b)²=9a²-1.2ab+0.04b²
е) (0.1x+2y)²=0.01x²+0.4xy+4y²
ж) (a-1)(a²+a+1)=a³-1
з) (y+2)(y²-2y+4)=y³+8

2.
a) 100-9x²=(10-3x)(10+3x)
б) 4a²+20ab+25b²=(2a+5b)²
в) 1/4 m² -m+1=(1/2 m -1)²
г) x³-1=(x-1)(x²+x+1)
д) 8+m⁶=(2+m²)(4-2m²+m⁴)
е) -0.25y⁴+49=(7-0.5y²)(7+0.5y²)

3.
a) (-x-5)²+(x-4)(-x-4)+(x-3)(x+7)=(-1*(x+5))²+(x-4)*(-1)*(x+4)+(x²-3x+7x-21)=
=(x+5)²-(x-4)(x+4)+x²+4x-21=x²+10x+25-x²+16+x²+4x-21=x²+14x+20

б) (x-1)(x²+x+1)-(3+x)(9-3x+x²)=x³-1-(27+x³)=x³-1-27-x³= -28

4.
a) 4(3y+1)²-27=(4y+9)(4y-9)+2(5y+2)(2y-7)
4(9y²+6y+1)-27=16y²-81+(10y+4)(2y-7)
36y²+24y+4-27=16y²-81+20y²+8y-70y-28
36y²+24y-23=36y²-62y-109
36y²-36y²+24y+62y=-109+23
86y=-86
y= -1
Ответ: -1.

б) 64x² - (x-1)²=0
(8x-(x-1))(8x+(x-1))=0
(8x-x+1)(8x+x-1)=0
(7x+1)(9x-1)=0

1)7x+1=0
x= -1/7

2) 9x-1=0
x=1/9

Ответ: -1/7;  1/9. 

5.
(a-1)(a²+1)(a+1)(a⁴-a²+1)(a⁶-1)=
=(a²-1)(a²+1)(a⁴-a²+1)((a²)³ - 1³)=
=(a⁴-1)(a⁴+1-a²)(a²-1)(a⁴+a²+1)=
=(a⁴-1)(a²-1)(a⁴+1-a²)(a⁴+1+a²)=
=(a⁶-a²-a⁴+1)((a⁴+1)² - (a²)²)=
=(a⁶-a⁴-a²+1)(a⁸+2a⁴+1-a⁴)=(a⁶-a⁴-a²+1)(a⁸+a⁴+1)=
=a¹⁴-a¹²-a¹⁰+a⁸+a¹⁰-a⁸-a⁶+a⁴+a⁶-a⁴-a²+1=
=a¹⁴-a¹²-a²+1

6.
(2n+3)² - (2n-3)² = (2n+3-(2n-3))(2n+3+2n-3)=(2n+3-2n+3)*4n=
=6*4n=24n
При любом целом n.