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29 tháng 7 2018

1)  \(\left(x^2-9\right)^2+12x\left(x-3\right)^2=\left(x-3\right)^2\left(x+3\right)^2+12x\left(x-3\right)^2\)

\(=\left(x-3\right)^2\left[\left(x+3\right)^2+12x\right]=\left(x-3\right)^2\left(x^2+6x+9+12x\right)\)

\(=\left(x-3\right)^2\left(x^2+18x+9\right)\)

\(=\left(x-3\right)^2\left[\left(x+9\right)^2-72\right]\)

\(=\left(x-3\right)^2\left(x+9-\sqrt{72}\right)\left(x+9+\sqrt{72}\right)\)

29 tháng 7 2018

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

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

\(=3\left(a+b\right)\left[ab+c\left(a+b+c\right)\right]\)

\(=3\left(a+b\right)\left(ab+bc+ca+c^2\right)\)

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

16 tháng 6 2018

a) a3+a2c-abc+b2c+b=(a3+b3)+(a2c-abc+b2c)=(a+b)(a2-ab+b2)+c(a2-ab+b2)=(a2-ab+b2)(a+b-c)

b) x3-7x-6 = x3+x2-x2-x-6x-6=x2(x+1)-x(x+1)-6(x+1)=(x+1)(x2-x-6)=(x+1)(x-3)(x+2)

c) x3-x2-14x+24=x3-2x2+x2-2x-12x+24=x2(x-2)+x(x-2)-12(x-2)=(x-2)(x2+x-12)=(x-2)(x+4)(x-3)

17 tháng 6 2018

Thank bn. 

26 tháng 7 2016

a) = (x-3)(x+3) +(x-3((x-3)

    = (x-3)(x+3+x-3) 

    = 2x(x-3)

làm cho 1 câu thui

25 tháng 6 2016

\(a,8x^3+12x^2y+6xy^2+y^3=\left(2x\right)^3+3.\left(2x\right)^2.y+3.2x.y^2+y^3=\left(2x+y\right)^3\)

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

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

16 tháng 7 2015

b) \(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

 

16 tháng 5 2017

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

31 tháng 10 2015

a/ = (x2 - 9) + (x - 3)2

= (x - 3)(x + 3) + (x - 3)2

= (x - 3)(x + 3 + x - 3)

= 2x(x - 3)

b/ = x3 - 7x2 + 9x + 3x2 - 21x + 27

= x(x2 - 7x + 9) + 3(x2 - 7x + 9)

= (x + 3)(x2 - 7x + 9)

c/ = x2 - 3x + 6x - 18

= x(x - 3) + 6(x - 3)

= (x + 6)(x - 3)

8 tháng 8 2016

a, x^2 -4+ (x-2)^2=(x-2)(x+2)+(x-2)^2=(x-2)(x+2+x-2)=(x-2)2x , b, x^3-2x^2+x-xy^2=x(x^2-2x+1-y^2)=x((x-1)^2-y^2)=x(x-1-y)(x-1+y)    c,x^3-4x^2-4x^2-12x+27=(x^3+27)-(4x^2+12x)=(x+3)(x^2-3x+9)-4x(x+3)=(x+3)(x^2-7x+9)                                                                                               cách giải đó pn.......

a) x2 - 4 + (x - 2)2

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

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

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

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

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

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

b) x3 - 2x2 + x - xy2

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

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

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

\(=x\left[\left(x-1-y\right)\left(x-1+y\right)\right]\)

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

c) x3 - 4x2 - 12x + 27

\(=\left(x^3+27\right)-\left(4x^2+12x\right)\)

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

\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)

\(=\left(x+3\right)\left[\left(x^2-3x+9\right)-4x\right]\)

\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)

\(=\left(x+3\right)\left(x^2-7x+9\right)\)

16 tháng 6 2018

\(a^3+a^2c-abc+b^2c+b^3\)

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

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

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

16 tháng 6 2018

thank bn

12 tháng 8 2016

a) x3 - x2 - 5x + 125

=(x3-6x2+25x)+(5x2-30x+125)

=x(x2-6x+25)+5(x2-6x+25)

=(x+5)(x2-6x+25)

b) x3 + 2x2 - 6x - 27

=x3+5x2+9-3x2-15x-27

=x(x2+5x+9)-3(x2+5x+9)

=(x-3)(x2+5x+9)

c) 12x3 + 4x2 - 27x - 9

=4x2(3x+1)-9(3x+1)

=(4x2-9)(3x+1)

=[(2x)2-32](3x+1)

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

 

12 tháng 8 2016

a) \(x^3-x^2-5x+125\)

\(=\left(x^3+125\right)-\left(x^2+5x\right)\)

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

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

b) \(x^3+2x^2-6x-27\)

\(=\left(x^3-27\right)+\left(2x^2-6x\right)\)

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

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

\(=\left(x-3\right)\left(x^2+5x+9\right)\)

c) \(12x^3+4x^2-27x-9\)

\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)

\(=\left(3x-1\right)\left(4x^2-9\right)=\left(3x-1\right)\left(2x-3\right)\left(2x+3\right)\)