Разложите ** множители: 1)...

Question

Разложите на множители:

1) 28-7y^2

2)-11x^2+22x-11

3)x^3y+8y

4)(y^2-1)^2-9

5)2m^3-18m

6)7m^2+14mn+7n^2

7) 6n^3+6m^3

8)16m^4-81n^4

Answer 1

1) 28-7y^2 = 7(4-у²)=7(2-у)(2+у)=-7(у+2)(у-2)

 

2) -11x^2+22x-11 = -11(х²-2х+1)=-11(х-1)²

 

3) x^3y+8y = у(х³+8)=у(х+2)(х²-2х+4)

 

4) (y^2-1)^2-9=(у²-1)²-3²=(у²-1-3)(у²-1+3)=(у²-4)(у²+2)=(у²+2)(у+2)(у-2)

 

5) 2m^3-18m = 2m(m²-9)=2m(m-3)(m+3)

 

6) 7m^2+14mn+7n^2 = 7(m²+2mn+n²)=7(m+n)²

 

7) 6n^3+6m^3 =6(n³+m³)=6(n+m)(n²-mn-m²)

 

8) 16m^4-81n^4 = (4m²)²-(9n²)²=(4m²+9n²)(4m²-9n²)=(4m²+9n²)(2m+3n)(2m-3n)