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16 tháng 8 2016

Đặt x2 + 4x + 8 = A. Ta sẽ được:

A2 + 3xA + 2x2 

= A2 - xA - 2xA + 2x2

= A(A-x) - 2x(A-x)

= (A-x)(A-2x)

= (x2+3x+8)(x2+2x+8)

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

\(=\left(x-y\right)\left[\left(x-y\right)+4\right]-12\)

\(=\left(x-y\right)\left(x-y+4\right)-12\)

f)  \(x^2-2xy+y^2+3x-3y-10\)

\(=\left(x^2-2xy+y^2\right)+\left(3x-3y\right)-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

\(=\left(x-y\right)\left[\left(x-y\right)+3\right]-10\)

\(=\left(x-y\right)\left(x-y+3\right)-10\)

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

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

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

\(=\left(x^2+4x+8\right)\left(x^2+7x+8\right)+2x^2\)

19 tháng 7 2016

a,\(x^2+4x-25y^2+4=\left(x^2+4x+4\right)-\left(5y\right)^2=\left(x+2\right)^2-\left(5y\right)^2\)

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

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

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

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

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

\(=\left(x-1\right)\left(4x+1\right)\)

19 tháng 7 2016

Mk làm sai câu b nha , phảo làm như sau 

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

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

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

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

2 tháng 8 2016

a, \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

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

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

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

\(=\left(x+3\right)\text{[}x\left(x+1\right)+2\left(x+1\right)\text{]}\)

\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

b, \(2x^3+3x^2+3x+2\)

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

\(=2x^2\left(x+1\right)+x\left(x+1\right)+2\left(x+1\right)\)

\(=\left(x+1\right)\left(2x^2+x+2\right)\)

c, \(x^3-4x^2-8x+8\)

\(=x^3+2x^2-6x^2-12x+4x+8\)

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

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

8 tháng 10 2018

\(A=\left(x^2+3x\right)^2-2\left(x^2+3x\right)-8=\left[\left(x^2+3x\right)^2-2\left(x^2+3x\right)+1\right]-9=\left(x^2+3x-1\right)^2-3^2\)

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

B tương tự

b. x4 - x2 - 2x - 1

=x4-(x2+2x+1)

=x4-(x+1)2

=(x2-x-1)(x2+x+1)

d. ( x2 + 3x + 1 ) ( x2 + 3x - 3 ) - 5

Đặt x2+3x=y

=> (y+1)(y-3)-5=y2-2y-8=(y-1)2-9

=(y-4)(y+2)

=(x2+3x-4)(x2+3x+2)=(x-1)(x+4)(x+1)(x+2)

12 tháng 12 2018

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

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

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

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

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

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

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

\(=\left(3-x\right),\left(x+4\right)\)