a: \(=9xy\left(y-2x\right)\)

b: \(=2\left(3x^2-y\right)\)

c: \(=7x\left(x-y\right)+14y\left(x-y\right)=7\left(x-y\right)\left(x+2y\right)\)

d: \(=\left(\sqrt{7}-x\right)\left(\sqrt{7}+x\right)\)

e: \(=\left(x+4\right)^2\)

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

g: \(=\left(x-3\right)^3\)

\(a.9xy^2-18x^2y=9xy\left(y-2x\right)\)

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

\(c.7x\left(x-y\right)-14y\left(y-x\right)=7x\left(x-y\right)+14y\left(x-y\right)=7\left(x-y\right)\left(x+2y\right)\)

\(d.7-x^2=\left(\sqrt{7}-x\right)\left(\sqrt{7}+x\right)\)

\(e.16+8x+x^2=\left(x+4\right)^2=\left(x+4\right)\left(x+4\right)\)

\(f.1-27x^3=\left(1-3x\right)\left(1+3x+9x^2\right)\)

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

\(h.\left(x+2y\right)^2-16y^2=\left(x+2y-4y\right)\left(x+2y+4y\right)=\left(x-2y\right)\left(x+6y\right)\)

\(i.x^3-64y^3=\left(x-4y\right)\left(x^2+4xy+16y^2\right)\)

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

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

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

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

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

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

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

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 ) 

a: \(5x-20y=5\left(x-4y\right)\)

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

c: \(x\left(x+y\right)-\left(5x+5y\right)=\left(x+y\right)\left(x-5\right)\)

d: \(5\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(y+5\right)\)

\(10x\left(x-y\right)-6y\left(y-x\right)\)

\(=10x\left(x-y\right)+6x\left(x-y\right)\)

\(=\left(10x+6x\right)\left(x-y\right)\)

\(c,3x^2+5y-3xy-5x\)

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

\(=3x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(3x-5\right)\left(x-y\right)\)

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

\(f,8x^3-12x^2y+6xy^2-y^3\)

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

\(g,x^3+8y^3=x^3+\left(2y\right)^3\)

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

\(i,x^2-25-2xy+y^2\)

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

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

d)5.(x-y)-y(x-y)

=(x-y)(5-y)

e) y.(x-z)+7(z-x)

=y.(x-z)-7(x-z)

=(x-z)(y-7)