Bài làm:

a, 1-4x²

=1-(2x)²

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

b, 8-27x³

=2³-(3x)³

=(2-3x).(4+6x+9x²)

Các câu còn lại bạn dùng hằng đẳng thức là phân tích được ra thôi

1 - 4x^2 

= 1^2 - ( 2x )^2 

= ( 1 - 2x ) ( 1 + 2x ) 

8 - 27x^ 3 

= 2^3 - ( 3x )^3 

= ( 2 - 3x ) [ 2^2 + 2 * 3x + ( 3x )^2 ]

= ( 2 - 3x ) ( 4 + 6x + 9x^2 ) 

= ( 2 - 3x ) ( 9x^2 + 6x + 4 ) 

27 + 27x + 9x^2 + x^3 

= x^3 + 9x^2 + 27x + 27 

= x^3 + 3x^2 + 6x^2 + 18x + 9x + 27 

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

= ( x + 3 ) ( x^2 + 6x + 9 ) 

= ( x + 3 ) ( x + 3 )^2 

= ( x + 3 )^3 

x^2 + 4x - 5 

= x^2 - x + 5x - 5 

= x ( x - 1 ) + 5 ( x - 1 ) 

= ( x + 1 ) ( x - 5 ) 

\(-x^3+9x^2-27x+27=\left(3-x\right)^3\)

\(-x^3+9x^2-27x+27\)

\(=-x^3+3x^2+6x^2-18x-9x+27\)

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

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

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

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

a) =( x²+y²-5)²-[2(xy-2)]²

⁼( x²+y²-5)²- (2xy-4)²

=(x²+y²-5+2xy-4)(x²+y²-5-2xy+4)

=[(x+y)²-9][(x-y)²-1]

phân tích tiếp HĐT 2 ở 2 thừa số

\(\left(x-1\right)^2-25\)

\(=x^2-2x+1-25\)

\(=x^2-2x-24\)

\(=x^2-6x+4x-24\)

\(=x.\left(x-6\right)+4.\left(x-6\right)\)

\(=\left(x+4\right).\left(x-6\right)\)

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

b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

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

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

a)=(1-y)²

b)=(x+1)²-5²

=(x+1+5)(x+1-5)

=(x+6)(x-4)

c)=1²-(2x)²

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

d)=2³-(3x)³

=(2-3x)(4+6x+9x²)

e)=3³+3.9.x+3.3.x²+x³

=(3+x)³

Câu c đề sai thì phải bạn ạ.

a) \(27+x^3=\left(x+3\right)\left(x^2-3x+9\right)\)

b) \(-x^3+12x^2-48x+64=\left(4-x\right)^3\)

c) \(27+27x+9x^2=9\left(x^2+3x+3\right)\)

\(27+27x+9x^2+x^3\)

\(=x^3+9x^2+27x+27\)

\(=x^3+3x^2+6x^2+18x+9x+27\)

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

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

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

Nếu nhìn kĩ thì bạn sẽ thấy đây là hằng đẳng thức nhé !

\(x^3+9x^2+27x+27=x^3+3.3.x^2+3.3^2.x+3^3\)

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

= (x+3)³

27+27x+9x²+x³

= x³+27x+9x²+27

=(x+3)³

CHÚC BẠN HỌC TỐT

a) \(-x^3+9x^2-27x+27=-\left(x^3-3.3.x^2+3.3^2.x-3^3\right)=-\left(x-3\right)^3\)

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

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

c)\(8x^3+27y^3+36x^2y+54xy^2=\left(2x\right)^3+3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2+\left(3y\right)^3\)

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