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dashagirina
@dashagirina
July 2022
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8
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ПОМОГИТЕ ПОЖАЛУЙСТА.....
Разложите множетель на многочлен
x³y²-xy²-x³+x.
ac⁴-c⁴-ac²+c².
-8a5степень+8a³-2a.
m³+27n³+m²+6mn+9n².
b6степень-4b⁴+12b²-9.
x5степень-2x⁴+x³-8x²+16x-8.
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Answers & Comments
m11m
Verified answer
1) x³y²-xy²-x³+x=(x³y²-xy²)-(x³-x)=xy²(x²-1)-x(x²-1)=
=(xy²-x)(x²-1)=x(y²-1)(x-1)(x+1)=x(y-1)(y+1)(x-1)(x+1)
2) ac⁴-c⁴-ac²+c²=c²(ac²-c²-a+1)=c²((ac²-c²)-(a-1))=
=c²(c²(a-1)-(a-1))=c²(a-1)(c²-1)=c²(a-1)(c-1)(c+1)
3) -8a⁵+8a³-2a= -2a(4a⁴-4a²+1)= -2a(2a-1)²
4) m³+27n³+m²+6mn+9n²=(m³+27n³)+(m²+6mn+9n²)=
=(m+3n)(m²-3mn+9n²)+(m+3n)²=
=(m+3n)(m²-3mn+9n²+m+3n)
5) b⁶-4b⁴+12b²-9=b⁶-(4b⁴-12b²+9)=b⁶-(2b²-3)²=(b³)² - (2b²-3)²=
=(b³-2b²+3)(b³+2b²-3)
6) x⁵-2x⁴+x³-8x²+16x-8=(x⁵-2x⁴+x³)-(8x²-16x+8)=x³(x²-2x+1)-8(x²-2x+1)=
=(x²-2x+1)(x³-8)=(x-1)²(x-2)(x²+2x+4)
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Answers & Comments
Verified answer
1) x³y²-xy²-x³+x=(x³y²-xy²)-(x³-x)=xy²(x²-1)-x(x²-1)==(xy²-x)(x²-1)=x(y²-1)(x-1)(x+1)=x(y-1)(y+1)(x-1)(x+1)
2) ac⁴-c⁴-ac²+c²=c²(ac²-c²-a+1)=c²((ac²-c²)-(a-1))=
=c²(c²(a-1)-(a-1))=c²(a-1)(c²-1)=c²(a-1)(c-1)(c+1)
3) -8a⁵+8a³-2a= -2a(4a⁴-4a²+1)= -2a(2a-1)²
4) m³+27n³+m²+6mn+9n²=(m³+27n³)+(m²+6mn+9n²)=
=(m+3n)(m²-3mn+9n²)+(m+3n)²=
=(m+3n)(m²-3mn+9n²+m+3n)
5) b⁶-4b⁴+12b²-9=b⁶-(4b⁴-12b²+9)=b⁶-(2b²-3)²=(b³)² - (2b²-3)²=
=(b³-2b²+3)(b³+2b²-3)
6) x⁵-2x⁴+x³-8x²+16x-8=(x⁵-2x⁴+x³)-(8x²-16x+8)=x³(x²-2x+1)-8(x²-2x+1)=
=(x²-2x+1)(x³-8)=(x-1)²(x-2)(x²+2x+4)