1: \(\left(x-2\right)^2-4x+8\)

\(=\left(x-2\right)\left(x-2-4\right)\)

\(=\left(x-2\right)\left(x-6\right)\)

3: \(a^3+6a^2+9a-ab^2\)

\(=a\left(a^2+6a+9-b^2\right)\)

\(=a\left(a+3-b\right)\left(a+3+b\right)\)

\(8^{13}-9.8^{12}+9.8^{11}-9.8^{10}+.....-9.8^2+9.8-2\)

\(=8^{13}-\left(8+1\right).8^{12}+\left(8+1\right).8^{11}-\left(8+1\right).8^{10}+....-\left(8+1\right).8^2+\left(8+1\right).8-2\)

\(=8^{13}-8^{13}-8^{12}+8^{12}+8^{11}-8^{11}-8^{10}+....-8^3-8^2+8^2+8-2\)

\(=\left(8^{13}-8^{13}\right)-\left(8^{12}-8^{12}\right)+\left(8^{11}-8^{11}\right)-....-\left(8^2-8^2\right)+8-2\)

\(=8-2=6\)

Cảm ơn cậu =))

a) 4(x+1)-(3x+1)=14

<=>4x+4-3x-1=14

<=>4x-3x = 14-4

<=>x=10

b) -12(x-5) +7.(3x)=5

<=> -12x +60 + 21+7x=5

<=> -12x+7x=5-60-21

<=> -5x=-76

<=> x=76/5

c) 17x + 34 -4x+28-9x=82

<=> 17x-9x-4x=82-34-28

<=> 4x=20

<=> x=5

cần trình bày cách làm không bạn?

a) x=11

b) x=-55/5

c) x= 5

a)Đặt \(A=3x^2-x+1\)

          \(A=3\left(x^2-2.\frac{1}{6}x+\frac{1}{36}\right)+\frac{11}{12}\)

            \(A=3\left(x-\frac{1}{6}\right)^2+\frac{11}{12}\)

                   Vì \(3\left(x-\frac{1}{6}\right)^2\ge0\Rightarrow3\left(x-\frac{1}{6}\right)^2+\frac{11}{12}\ge\frac{11}{12}\)

Dấu = xảy ra khi \(x-\frac{1}{6}=0\Rightarrow x=\frac{1}{6}\)

         Vậy Min A = \(\frac{11}{12}\) khi x=1/6

b)Tương tụ

x=8 nên x+1=9

\(F=x^{13}-9x^{12}+9x^{11}-9x^{10}+...-9x^2+9x-2\)

\(=x^{13}-x^{12}\left(x+1\right)+x^{11}\left(x+1\right)-x^{10}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-2\)

\(=x^{13}-x^{13}-x^{12}+x^{12}+...-x^3-x^2+x^2+x-2\)

=x-2

=8-2

=6

Để F(x) có nghiệm <=> x^10 - 9x^9 + ... + 9x^2 - 9x +8 = 0

<=> (x^10 - x^9) - (8x^9 - 8x^8) + (x^8 - x^7) - ... + (x^2 - x) - (8x - 8) = 0

<=> x^9(x - 1) - 8x^8(x - 1) + ... + x(x - 1) - 8(x - 1) = 0

<=> (x^9 - 8x^8 + ... + x - 8)(x - 1) = 0

<=> (  (x^9 - 8x^8) + (x^7 - 8x^6) + ... + (x - 8)  )(x - 1) = 0

<=> (x^8 + x^6 + ... + 1)(x - 8)(x - 1) = 0

Có nghiệm là 8 và 1

a) x= - 15

b) x= - 2

c) x= -12 

d) x= -2