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18 tháng 8 2020

1)\(8x^6-\frac{1}{125}y^3=\left(2x^2\right)^3-\left(\frac{1}{5}y\right)^3\)

Bạn tự lm tiếp.AD HĐT số (7)

2)\(\left(x+4\right)^3-64=\left(x+4\right)^3-4^3\)

AD HĐT số (7).Tự lm tiếp

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

AD HĐT số (7).Tự lm tiếp

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

AD HĐT số (7).Tự lm tiếp

5,\(x^{12}-y^4=\left(x^6\right)^2-\left(y^2\right)^2\)

AD HĐT số (3).Tự lm tiếp

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

AD HĐT số (4)

7)\(x^3-15x^2+75x-125=\left(x-5\right)^3\)

AD HĐT số (5)

8)\(27a^3-54a^2b+36ab^2-8b^3\)

\(=\left(3a\right)^3-3.\left(3a\right)^2.2b+3.3a.\left(2b\right)^2-\left(2b\right)^3\)

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

AD HĐT số (5)

17 tháng 7 2018

1. \(\left(x+1\right)^3-125\)

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

\(=\left(x+1-5\right).\left[\left(x+1\right)^2+\left(x+1\right).5+5^2\right]\)

2. \(\left(x+4\right)^3-64\)

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

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

3. \(x^3-\left(y-1\right)^3\)

\(=(x^3-y+1).\left[\left(x^2\right)+x.\left(y+1\right)+\left(y+1\right)^2\right]\)

\(\)4. \(\left(a+b\right)^3-c^3\)

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

5. \(125-\left(x+2\right)^3\)

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

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

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

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

23 tháng 7 2023

\(a,\left(x-1\right)^2-2^2=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\\ b,=\left(2x\right)^2+2.2x.3+3^2\\ =\left(2x+3\right)^2\\ c,=x^3-\left(2y\right)^3\\ =\left(x-2y\right)\left(x^2+2xy+4y^2\right)\\ d,=x^3\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^3-1\right)\left(x^2-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\)

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

\(f,=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1^2+1^3\\ =\left(2x+1\right)^3\)

4 tháng 7 2021

1) x2 -7x + 10 = x2 - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)

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

3) x2 - 7x + 12 = x2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)

4) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)

5) 16x - 5x2 - 3 = 15x - 5x2 + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x) 

6) 6x2 + 7x - 3 = 6x2 - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)  

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

8) 3x2 + 3x - 6 = 3x2 - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)

9) 6x2 - 13x + 6 = 6x2 - 9x -  4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3) 

10) 6x2 + 15x  + 6 = 6x2 + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)

11) 6x2 - 20x + 6 = 6x2 - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)

12) 8x2 + 5x - 3 = 8x2 + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)

9 tháng 8 2017

3)(9a)2-(5a-3b)2

= (9a-5a+3b)(9a+5a-3b)

= (4a+3b)(14a-3b)

18 tháng 10 2018

16x4y2-25a2b2

16 tháng 10 2019

1) \(x^6+1\)

\(=x^6+x^4-x^4+x^2-x^2+1\)

\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)

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

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

2) \(x^6-y^6\)

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

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

30 tháng 7 2018

b)  \(64x^3+1=\left(4x+1\right)\left(16x^2-4x+1\right)\)\

c) \(x^3y^6z^9-125=\left(xy^2z^3-5\right)\left(x^2y^4z^6+5xy^2z+25\right)\)

d)  \(27x^6-8x^3=x^3\left(27x^3-8\right)=x^3\left(3x-2\right)\left(9x^2+6x+4\right)\)

e)  \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

64x3 + 1

= ( 4x )3  +  1

= ( 4x + 1 ) ( 16x2 - 4x + 1 )

Hằng đẳng thức 6 : A3 + B3

27x6 - 8x3

= ( 3x2)3 + ( 2x )3

= ( 3x + 2x ) ( 9x2 - 6x + 4x2 )

HĐT 6

x6 - y6

= ( x2 )3 - ( y2 )3

= ( x2 - y2 ) ( x4 + x2y2 + y4 )

HĐT 7 : A3 - B3

x3y6z9 + 1

= ( xy2z3)3 + 1

= ( xy2z3 + 1 ) ( x2y4z6 + zy2z3 + 1 )

HĐT 6

31 tháng 7 2018

b, <=>(4x)3+13 

<=> (4x+1)( 16x2-4x+1)

c, <=> (x.y2.z3)3-53

<=> (xy2z3-5)( x2y4z6+5xy2z3+25)

d, <=> (3x2)3-(2x)3

<=> (3x2-2x)(9x4+6x3+4x2)

d, (x3)2- (y3)2 

= (x3+y3)(x3-y3)