Объяснение:
4.
а) x³-9x=x(x²-9)=x(x-3)(x+3)
б) -5a²-10ab-5b²=-5(a²+2ab+b²)=-5(a+b)²
в) 16х⁴-81=(4х²-9)(4х²+9)=(2х-3)(2х+3)(4х²+9)
г) х²+х-у²-у=х(х+1)-у(у+1)=(х-у)(у+1)
д) х²-6х+9-d²=(x-3)²-d²=(x-3+d)(x-3-d)
е) 27p³+q³-9p²+3pq-q²=(3p+q)(9p²-3pq+q²)-(9p²-3pq+q²)=(3p+q-1)(9p²-3pq+q²)
5.
а) 5x⁴-125x²=0
x²=t, t≥0
5t²-125t=0
5t(t-25)=0
t=0, x²=0, x=0
t=25, x²=25, x₁=5, x₂=-5
б) x²-6x+8=0
D=36-32=4
x₁=(6+2)/2=4
x₂=(6-2)/2=2
в) 36m⁴-36m²-12m³+12m=0
3m⁴-3m²-m³+m=0
3m²(m²-1)-m(m²-1)=0
(m²-1)(3m²-m)=0
m(3m-1)(m-1)(m+1)=0
m₁=0, m₂=1/3, m₃=1, m₄=-1
Объяснение:
4.
а) x³-9x=x(x²-9)=x(x-3)(x+3)
б) -5a²-10ab-5b²=-5(a²+2ab+b²)=-5(a+b)²
в) 16х⁴-81=(4х²-9)(4х²+9)=(2х-3)(2х+3)(4х²+9)
г) х²+х-у²-у=х(х+1)-у(у+1)=(х-у)(у+1)
д) х²-6х+9-d²=(x-3)²-d²=(x-3+d)(x-3-d)
е) 27p³+q³-9p²+3pq-q²=(3p+q)(9p²-3pq+q²)-(9p²-3pq+q²)=(3p+q-1)(9p²-3pq+q²)
5.
а) 5x⁴-125x²=0
x²=t, t≥0
5t²-125t=0
5t(t-25)=0
t=0, x²=0, x=0
t=25, x²=25, x₁=5, x₂=-5
б) x²-6x+8=0
D=36-32=4
x₁=(6+2)/2=4
x₂=(6-2)/2=2
в) 36m⁴-36m²-12m³+12m=0
3m⁴-3m²-m³+m=0
3m²(m²-1)-m(m²-1)=0
(m²-1)(3m²-m)=0
m(3m-1)(m-1)(m+1)=0
m₁=0, m₂=1/3, m₃=1, m₄=-1