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

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

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

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

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

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

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

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

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

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

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

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

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

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

hết hk 1 r đó

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(h.\left(x^2+1\right)^2-4x^2\\ =\left(x^2+1\right)^2-\left(2x\right)^2\\ =\left[\left(x^2+1\right)-2x\right]\left[\left(x^2+1\right)+2x\right]\\ =\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)

Lần sau bạn nhấp vào kí hiệu Σ để gõ công thức nha .

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

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

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

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

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

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

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

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

\(\Leftrightarrow y^2-2y+1\)

\(\Leftrightarrow\left(y-1\right)^2\)

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

\(\Leftrightarrow\left(x+1\right)^2-5^2\)

\(\Leftrightarrow\left(x-4\right)\left(x+6\right)\)

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

\(\Leftrightarrow1-\left(2x\right)^2\)

\(\Leftrightarrow\left(1-2x\right)\left(1+2x\right)\)

\(\left(d\right)8-27x^3\)

\(\Leftrightarrow2^3-\left(3x\right)^3\)

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

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

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

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

\(\Leftrightarrow\left(2x\right)^3-12x^2y+6xy^2-y^3\)

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

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

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

a) 1 - 2y + y2

=> (1-y)

b) ( x + 1 )2 - 25

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

=>(x-4)(x+6)

c) 1 - 4x²

=>1²-2²x²

=>1²(2x)²

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

d) 8 - 27x³

=>2³-3³x³

=>2³(3x)³

=>(2-3x)[2²+2.3x+(3x)²]

=>(2-3x)(4+6x+9x²)

e) 27 + 27x + 9x2 + x³

=>(3+x)³

f) 8x3 - 12x2y + 6xy2 - y3

=>2x(4x²6x+3)

g) x3 + 8y3

=>x³+(2y)³

=>(x+2y)[x²-x.2y+(2y)²]

=>(x+2y)(x²-2xy+4y²)

a) 1 - 2y + y²

= (1-y)²

b) ( x + 1 )² - 25

=( x + 1 )² - 5²

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

c) 1 - 4x²

= 1- 2x²

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

a) \(1-2y+y^2\)

\(=y^2-2\cdot y\cdot1+1^2\)

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

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) \(8-27x^3\)

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

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

e) \(27+27x+9x^2+x^3\)

\(=3^3+3\cdot3^2\cdot x+3\cdot3\cdot x^2+x^3\)

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

f) \(8x^3-12x^2y+6xy^2-y^3\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3\)

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

g) \(x^3+8y^3\)

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

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

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

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

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

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

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

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

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

Tham khảo nhé~

Mấy cái này chỉ áp dụng HĐT thoyy nha!

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

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

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

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

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

\(f,8x^3-12x^2y+9xy^2-y^3=\left(2x-y\right)^2\)

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

=.= hok tốt!!

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

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

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

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

\(d,8-27^3=2^3-27^3=\left(2-27\right)\left(2^2+2.27+27^2\right)\)

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

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

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

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