Разложите на множители: 1) 28-7y^2 2)-11x^2+22x-11 - вопрос №151421812872211222113384212 от V369906 09.02.2021 10:17

Question

Алгебра: 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

V369906 · Answer

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)