№1
а) 18a²-2=2(9a²-1)=2(3a-1)(3a+1)
б) 2ax³-16ay³=2a(x³-8y³)=2a(x-2y)(x²+2xy+y²)
в) 8k⁴+8k²+2=2(4k⁴+4k²+1)=2(2k²+1)
г) 9m²-6m-10p-25p²=(9m²-25p²)-(6m+10p)=(3m-5p)(3m+5p)-2(3m+5p)=
=(3m+5p)(3m-5p-2)
д)a³+3a²x+6ax+12x-8=(a³-8)+3x(a²+2a+4)=(a-2)(a²+2a+4)+3x(a²+2a+4)=
<span> =(a²+2a+4)(a-2+3x)
№2
x(x+y)</span>²-y(x-y)²+2y(x²+y²)=x(x²+2xy+y²)-y(x²-2xy+y²)+2x²y+2y³=x³+2x²y+xy²-x²y+2xy²-y³+2x²y+2y³=x³+3x²y+3xy²+y³=(x+y)³
(2,5+0,5)³=3³=27<span>
№3
x(5x+x)(x-5)-(x-3)(x</span>²+3x+9)=-23
<span>x(5x-25+x</span>²-5x)-(x³-3x²+3x²-9x+9x-27)=-23
-25x+x³-x³+27=-23
<span>-25x=-50
x=2
№4
</span>
=
=-1<span>
№5
</span>a²+4ab+3b²=a²+ab+3ab+b²=a(a+b)+3b(a+b)=(a+b)(a+3b)
а) 18a²-2=2(9a²-1)=2(3a-1)(3a+1)
б) 2ax³-16ay³=2a(x³-8y³)=2a(x-2y)(x²+2xy+y²)
в) 8k⁴+8k²+2=2(4k⁴+4k²+1)=2(2k²+1)
г) 9m²-6m-10p-25p²=(9m²-25p²)-(6m+10p)=(3m-5p)(3m+5p)-2(3m+5p)=
=(3m+5p)(3m-5p-2)
д)a³+3a²x+6ax+12x-8=(a³-8)+3x(a²+2a+4)=(a-2)(a²+2a+4)+3x(a²+2a+4)=
<span> =(a²+2a+4)(a-2+3x)
№2
x(x+y)</span>²-y(x-y)²+2y(x²+y²)=x(x²+2xy+y²)-y(x²-2xy+y²)+2x²y+2y³=x³+2x²y+xy²-x²y+2xy²-y³+2x²y+2y³=x³+3x²y+3xy²+y³=(x+y)³
(2,5+0,5)³=3³=27<span>
№3
x(5x+x)(x-5)-(x-3)(x</span>²+3x+9)=-23
<span>x(5x-25+x</span>²-5x)-(x³-3x²+3x²-9x+9x-27)=-23
-25x+x³-x³+27=-23
<span>-25x=-50
x=2
№4
</span>
№5
</span>a²+4ab+3b²=a²+ab+3ab+b²=a(a+b)+3b(a+b)=(a+b)(a+3b)