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

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

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

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

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

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

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

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

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 ) 

1

a, 2x²+4x+2-2y² = 2(x²+2x+1-y²)= 2[(x+1)²-y² ] = 2(x-y+1)(x+y+1)

b, 2x - 2y - x² + 2xy - y²= 2(x -y) - (x² - 2xy + y²) = 2(x-y)-(x-y)²=(x-y)(2-x+y)

c, x²-y²-2y-1=x²-(y²+2y+1)=x²-(y+1)²=(x-y-1)(x+y+1)

d, x²-4x-2xy-4y+y²= x²-2xy+y²-4x-4y=(x-y)

2.

a, x²-3x+2=x²-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)

b, x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)

c, x²+6x-6=

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

b)  \(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

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

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

1-2y+y²=(1-y)²

(x+1)²-25=(x+1-5)(x+1+5)=(x-4)(x+6)

1-4x²=(1-2x)(1+2x)

8-27x³=(2-3x)(4+6x+9x²)

\(a,=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\\ b,=\dfrac{1}{3}x\left(y+3xz+3z\right)\\ c,=2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)

\(d,=x^2\left(\dfrac{2}{5}+5x+y\right)\\ e,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ f,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ g,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)

1.A

2.C

3.B

4.C

a

c

b

c

(x-1)y^2-4(x-1)y

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

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

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

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

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

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

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

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!!

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

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

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

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

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

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

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

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

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