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18 tháng 8 2018

a) \(8x^3-27y^6\)

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

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

\(=\left(2x-3y^2\right)\left(4x^2+6xy+9y^2\right)\)

b) \(a^3b^3c^3-1\)

\(=\left(abc\right)^3-1^3\)

\(=\left(abc-1\right)\left(a^2b^2c^2+abc+1\right)\)

c) \(64x^3+\dfrac{1}{8}y^3\)

\(=\left(4x\right)^3+\left(\dfrac{1}{2}y\right)^3\)

\(=\left(4x+\dfrac{1}{2}y\right)\left[\left(4x\right)^2+4x.\dfrac{1}{2}y+\left(\dfrac{1}{2}y\right)^2\right]\)

\(=\left(4x+\dfrac{1}{2}y\right)\left(4x^2+2xy+\dfrac{1}{4}y^2\right)\)

d) \(125+y^3\)

\(=5^3+y^3\)

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

e) \(a^6-b^6\)

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

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

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

f) \(4x^2-9\left(3x+5\right)^2\)

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

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

\(=\left(2x-9x-15\right)\left(2x+9x+15\right)\)

\(=\left(-7x-15\right)\left(11x+15\right)\)

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

17 tháng 10 2016

a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)

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

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

\(=\left(a+7b\right)\left(5a-b\right)\)

b) \(9x^6-12x^7+4x^8\)

\(=x^6\left(9-12x+4x^2\right)\)

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

c) \(8x^6-27y^3\)

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

\(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)

d) \(\frac{1}{64}x^6-125y^3\)

\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)

\(=\left(\frac{1}{4}x^2-5y\right)\left(\frac{1}{16}x^4+\frac{5}{6}xy+25y^2\right)\)

13 tháng 9 2021

dấu ^ là mũ nha mn

 

3 tháng 8 2023

a) 9x4+16y6-24x2y3

=(3x2)2-2.3x2.4y3+(4y3)2

=(3x2-4y3)2

b) 16x2-24xy+9y2

=(4x)2-2.4x.3y+(3y)2

=(4x-3y)2

c) 36x2-(3x-2)2

=(36x-3x+2)(36x+3x-2)

=(33x+2)(39x-2)

d) 27x3+54x2y+36xy2+8y3

=(3x)3+3.(3x)2.2y+3.3x.(2y)2+(2y)3

=(3x+2y)3

e) y9-9x2y6+27x4y3-27x6

=(y3)3-3.(y3)2.3x2+3.y3.(3x2)2-(3x2)3

=(y3-3x2)3

f) 64x3+1

= (4x)3+13

=(4x+1)[(4x)2-4x.1+12]

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

e) 27x6-8x3  *sửa đề*

=(3x2)3-(2x)3

=(3x2-2x)[(3x)2+3x2.2x+(2x)2]

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

~~~

4 tháng 10 2017

8x3- 125= (2x)3- 53= (2x-5)[(2x)2+2x5+52 ]=(2x-5)(4x2+10x+25)

4 tháng 10 2017

\(8x^3-125\)

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

\(=\left(2x-5\right)\left(4x^2+10x+25\right)\)

9 tháng 10 2021

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

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

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

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

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

c) \(x^6-x^4+2x^3+2x^2=\left(x^6+2x^3+1\right)-\left(x^4-2x^2+1\right)\)

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

d) \(x^3+3x^2+3x+1-8y^3=\left(x+1\right)^3-8y^3=\left(x+1-2y\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)