Ответ:

Объяснение:

1.

12x³-27xy²=3x(4x²-9y²)=3x(2x-3y)(2x+3y)

2a³-16b³=2(a³-8b³)=2(a-2b)(a²+2ab+b²)

m⁵-8m³n+16mn²=m(m⁴-8m²n+16n²)=m(m²-4n)²

9x²+15x+25y-25y²=(3x-5y)(3x+5y)+5(3x+5y)=(3x+5y)(3x-5y+5)

y³+y²x-3yx+9x+27=(y+3)(y²-3y+9)+x(y²-3y+9)=(y²-3y+9)(x+y+3)

2.

(a²+a)(a-1)-(a-2)(a²+2a+4)=a(a+1)(a-1)-(a-2)(a²+2a+4)

При a=3 3/4=15/4:

15/4 ·(15/4 -1)(15/4 +1)-(15/4 -2)((15/4)²+2·15/4 +4)=15/4 ·11/4 ·19/4 -7/4 +15/2 +4=3135/64 +4 23/4=48 63/64 +9 3/4=48 63/64 +9 48/64=58 47/64

3.

-(3x-1)²+2(5+x)(x-5)+7x²=3

-(9x²-6x+1)+2(x²-25)+7x²=3

-9x²+6x-1+2x²-50+7x²=3

6x-51=3

x=54/6=9

4.

(53²+22²-47²-16²)/(65²-2·65·59+59²)=((53-47)(53+47)+(22-16)(22+16))/(65-59)²=(600+228)/36=828/36=23

5.

x⁴+3x²+4=x⁴+4x²-x²+4=(x²+2)²-x²=(x²-x+2)(x²+x+2)