(10√‎5-2√‎3) (10 √‎5+4 √‎3)

Question

Алгебра: (10√‎5-2√‎3) (10 √‎5+4 √‎3)

egordima2003 · Accepted 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)

MOGZ ответил