Разложите ** множители : 1. 1000m³-n³ 2. 81a³-ab² 3. -8x²-16xy-8y² 4. 5mn+15m-10n-30 5....

Question

Разложите на множители : 1. 1000m³-n³ 2. 81a³-ab² 3. -8x²-16xy-8y² 4. 5mn+15m-10n-30 5. 256-b⁴ упростите выражение: y(y-5)(y+5)-(y+2)(y²-2y+4)

Answer 1

1) (10m-n)(100m²+10mn+n²)

2) a(81a²-b²)= a(9a-b)(9a+b)

3) -8(x²+2xy+y²)= -8(x+y)²= -8(x+y)(x+y)

4) 5m(n+3)-10(n+3)= 5(m-2)(n+3)

5) (16-b²)(16+b²)= (4-b)(4+b)(16+b²)

6) y(y²-25)-(y³+8)= y³-25y-y³-8= -25y-8

Answer 2

1)1000m³-n³=(10m)³-n³

=(10m-n)(100m²+10mn+n²)

2)81a³-ab²=a((9a)²

-b²)=a(9a-b)(9a+b)

3)-8x²-16xy-8y²=-8(x²+2xy

+y²)=-8(x+y)²

4)5mn+15m-10n-30=

5(n+3m-2n-6)=

5(m(n+3)-2(n+3)=

5(n+3)(m-2)

5)256-b⁴=4⁴-b⁴=(4²-b²)(4²+b²)=

(4-b)(4+b)(16+b²)