Variant 1.
1.
p(x)=p₁(x)+p₂(x)=(x²+2)-(x³-x²-1)=x³+1
p₁(x)=x²+2
p₂(x)=x³-x²-1
2.
a)2x(x+1)=2x²+2x
b)x²y(x-y)=x³y-x²y²
3.
a)(x-2)²=x²-4x+4
b)(3x²+y²)²=9x⁴+6x²y²+y²
4.
((a⁵+2a⁴-a³)/(-a³))+(a-1)(a+1)=-4
(a-1)(a+1)=a²-a+a-1=a²-1
-(a⁵+2a⁴-a³)/(a³)=-(a³(a²+2a-1))/(a³)=-(a²+2a-1)
-a²-2a+1+a²-1=-2a
a=2
-2*2=-4
5.
(2x-3)(3x+2)=(x-1)(x+1)+(5x+2)(x-14)
(x-1)(x+1)=x²-1
(5x+2)(x-14)=5x²-70x+2x-28=5x²-68x-28
(2x-3)(3x+2)=6x²+4x-9x-6=6x²-5x-6
5x²-68x-28+x²-1=6x²-68x-29
6x²-5x-6=6x²-68x-29
63=-23
x=-23/63
Variant 2.
1.
p(x)=p₁(x)-p₂(x)=(x²+2x)-(x³+x²-2x)=-x³+4x
p₁(x)=x²+2x
p₂(x)=x³+x²-2x
2.
a)3x(x-2)=3x²-6x
b)x²y²(x+2y)=x³y²+2x²y³
3.
a)(2x+4)²=4x²+16x+16
b)(x²-2y²)²=x⁴-4x²y²+4y²
4.
((a²-a⁷+a³)/(-a²))+(a+1)²=-1
((a²-a⁷+a³)/(-a²))=-(a²(1-a⁵+a))/(a²)=a⁵-a-1
(a+1)²=a²+2a+1
a⁵-a-1+a²+2a+1=a⁵+a²+a
a=-1
(-1)⁵+(-1)²+(-1)=-1+1-1=-1
5.
4(x-4)(x+8)=(3x+2)(x-5)+(x-1)(x+1)
(x-1)(x+1)=x²-1
4(x-4)(x+8)=4(x²+8x-4x-32)=4(x²+4x-32)=4x²+16x-128
(3x+2)(x-5)=3x²-15x+2x-10=3x³-13x-10
3x³-13x-10+x²-1=4x²-13x-11
4x²+16x-128=4x²-13x-11
29x=117
x=117/29