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12 tháng 9 2018

 \(A=x^4-x^2+16\)

    \(=x^4+8x^2+16-9x^2\)

    \(=\left(x^2+4\right)^2-\left(3x\right)^2\)

    \(=\left(x^2-3x+4\right)\left(x^2+3x+4\right)\)

\(B=x^4+6x^2+25\)

   \(=x^4+10x^2+25-4x^2\)

   \(=\left(x^2+5\right)-\left(2x\right)^2\)

   \(=\left(x^2-2x+5\right)\left(x^2+2x+5\right)\)

\(C=4x^4-16-4x^2-16x\)

    \(=4x^2\left(x^2-1\right)-16\left(x+1\right)\)

    \(=4x^2\left(x-1\right)\left(x+1\right)-16\left(x+1\right)\)

    \(=\left(4x^2-4x\right)\left(x+1\right)-16\left(x+1\right)\)

     \(=\left(x+1\right)\left(4x^2-4x-16\right)\)

\(D=b^2-7bc+12c^2\)

    \(=b^2-3bc-4bc+12c^2\)

    \(=b\left(b-3c\right)-4c\left(b-3c\right)\)

     \(=\left(b-3c\right)\left(b-4c\right)\)

Chúc bạn học tốt.

30 tháng 10 2016

\(x^3-x^2-5x+125\)

\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)

\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)

\(=\left(x+5\right)\left(x^2-6x+25\right)\)

\(x^6-x^4-9x^3+9x^2\)

\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)

\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)

\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)

\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)

\(x^4-4x^3+8x^2-16x+16\)

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

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

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

\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4c^2\right)\)

\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)

30 tháng 10 2016

cảm ơn bạn nha!eoeo

24 tháng 7 2018

\(x^4-4x^3+8x^2-16x+16 \)

\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)

\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)

\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)

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

29 tháng 7 2020

Bài làm:

a) \(x^2-6x+4=\left(x^2-6x+9\right)-5=\left(x-3\right)^2-\left(\sqrt{5}\right)^2\)

\(=\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)

b) \(x^2-4x+3=x^2-x-3x+3=\left(x-1\right)\left(x-3\right)\)

c) \(6x^2-5x+1=6x^2-3x-2x+1=\left(2x-1\right)\left(3x-1\right)\)

d) \(3x^2+13x-10=3x^2+15x-2x-10=\left(x-5\right)\left(3x-2\right)\)

b mk thấy nó sai đề sao ý 

c) \(C=\left(x^2+x+4\right)^2+8x\left(x^2+x+4\right)+15x^2\)

\(=\left(x^2+x+4\right)^2+2.4x.\left(x^2+x+4\right)+16x^2-x^2\)

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

\(=\left(x^2+5x+4\right)^2-x^2\)

\(=\left(x^2+5x+4-x\right)\left(x^2+5x+4+x\right)=\left(x^2+4x+4\right)\left(x^2+6x+4\right)\)

2 tháng 8 2020

Bài làm:

a) \(x^6-6x^4+12x^2-8\)

\(=\left(x^2-2\right)^3\)

b) \(x^2+16-8x=\left(x-4\right)^2\)

c) \(10x-x^2-25=-\left(x-5\right)^2\)

d) \(9\left(a-b\right)^2-4\left(x-y\right)^2\)

\(=\left[3\left(a-b\right)\right]^2-\left[2\left(x-y\right)\right]^2\)

\(=\left(3a-3b-2x+2y\right)\left(3a-3b+2x-2y\right)\)

e) \(\left(x+y\right)^2-2xy+1\)

\(=x^2+2xy+y^2-2xy+1\)

\(=x^2+y^2+1\)

sai sai

2 tháng 8 2020

a.  \(x^6-6x^4+12x^2-8=\left(x^2\right)^3-3\left(x^2\right)^2.2+3x^22-2^3=\left(x^2-2\right)^3\)

b. \(x^2+16-8x=x^2-8x+4^2=\left(x-4\right)^2\)

c. \(10x-x^2-25=10x-x^2-5^2=-\left(x-5\right)^2\)

d. \(9\left(a-b\right)^2-4\left(x-y\right)^2=\left[3\left(x-y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x+y\right)\right]\)

\(=\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)=\left(x-5y\right)\left(5x-y\right)\)

e. \(\left(x+y\right)^2-2xy+1=x^2+2xy+y^2-2xy+1=x\left(x+2y\right)-y\left(y+2x\right)+2y^2+1\)

\(=x\left(x+y\right)-y\left(y+x\right)+xy-yx+2y^2+x=\left(x-y\right)\left(x+y\right)+2y^2+x\)

29 tháng 9 2018

Ý a) sại đề bài ak??

29 tháng 9 2018

       \(16x^4+y^4+4x^2y^2\)

\(=\left(4x^2\right)^2+2.4x^2.y^2+\left(y^2\right)^2-4x^2y^2\)

\(=\left(4x^2+y^2\right)-\left(2xy\right)^2\)

\(=\left(4x^2-2xy+y^2\right)\left(4x^2+2xy+y^2\right)\)

      \(x^3-2x-4\)

\(=x^3-2x^2+2x^2-4x+2x-4\)

\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+2x+2\right)\)

      \(x^3+x^2+4\)

\(=x^3+2x^2-x^2-2x+2x+4\)

\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-x+2\right)\)

11 tháng 12 2018

a, x^2-4x+3

=x^2-x-3x+3

=x(x-1)-3(x-1)

=(x-3)(x-1)

11 tháng 12 2018

\(\left(x^2+x\right)^2+4x^2+4x-12\)

\(=x^4+2x^3+5x^2+4x-12\)

\(=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12\)

\(=x^3.\left(x-1\right)+3x^2.\left(x-1\right)+8x.\left(x-1\right)+12.\left(x-1\right)\)

\(=\left(x-1\right).\left(x^3+3x^2+8x+12\right)=\left(x-1\right).\left(x+2\right).\left(x^2+x+6\right)\)

p/s: sai sót bỏ qua