данное выражение представьте в виде произведения числа и квадрата многочлена: а) 3х^2-6х+3 б)8а-8-2а^2 в)(3х+1)^2+2(3х+1)+1 г) (m^2+9m)+18(m^2+9)+81
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в) (3х+1+1)^2=(3х+2)^2.
г) (м^2+9м+9)^2.
D = 36 - 36 = 0
x = -b/2a = 6 /6 = 1.
⇒ 3(x-1)².
б) -2a² + 8a - 8
D = 64 - 64 = 0
a = -b/2a = -8/-4 = 2.
⇒ -2(a - 2)².
в) (3x + 1)² + 2(3x + 1) +1
9x² + 6x + 1 + 6x + 2 + 1
9x² + 12x + 4
D = 144 - 144 = 0
x = -b/2a = -12/18 = -2/3.
⇒ 9(x + 2/3)².
г) (m² + 9m) + 18(m² + 9) + 81
m² + 18m + 81
D = 324 - 324 = 0
m = -b/2a = -18/2 = -9.
⇒ (m+9)².