a)\(\left(3x-1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\)

                                     \(=\left(3x-17\right)\left(3x+15\right)\)

c)\(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)

                                                 \(=\left(x-4\right)\left(x+14\right)\)

      Aps dungj t/c a² - b² = ( a-b)(a+b)

a) \(\left(2x+5\right)^2\)\(-\left(x-9\right)^2\)

=\(\left(2x+5+x-9\right).\left(2x+5-x+9\right)\)

=\(\left(3x-4\right).\left(x+14\right)\)

a)x^2-(a+b)x+ab

= x^2 - ax - bx + ab

= (x^2 - ax) - (bx - ab)

= x(x-a) - b(x-a)

= (x-b)(x-a) 

b)7x^3-3xyz-21x^2+9z

= 

c)4x+4y-x^2(x+y)

= 4(x + y) - x^2(x+y)

= (4-x^2) (x+y)

= (2-x)(2+x)(x+y)

d) y^2+y-x^2+x

= (y^2 - x^2) + (x+y)

= (y-x)(y+x)+ (x+y)

= (y-x+1) (x+y)

e)4x^2-2x-y^2-y

= [(2x)^2 - y^2] - (2x +y)

= (2x-y)(2x+y) - (2x+y)

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

f)9x^2-25y^2-6x+10y

= 

ko biết làm

a) ( 3x -1 )²  - 16  

= (3x -1 ) ²  - 4² 

= ( 3x -1 -4 ).( 3x -1 +4 )

b)  ( 5x-4 ) ² - 49x² 

= ( 5x-4 ) ²   - (7x)²

=( 5x -4 -7x).( 5x -4 + 7x )

=( -2x -4 ) .( 12x -4 )

còn lại giống tương tự nha pạn 

~ hok tốt ~

a, ( 3x - 1 )² - 16

= (3x-1 ) ² - 4²

= [ 3x - 1 + 4 ] . [ 3x - 1 - 4 ]

 b, ( 5x - 4 )² - 49x²

⁼ ( 5x - 4 )²  - (7x)²

= [ 5x - 4 + 7x ] . [ 5x - 4 - 7x ]

c, 4x² - ( 2x - 5 )²

= (2x)² - ( 2x - 5 ) ²

= [ 2x + 2x - 5 ] . [ 2x - 2x - 5 ]

 Mik làm đầy đủ nhất nhé !!

 \(a.\left(3x-1\right)^2-16\)

\(\Leftrightarrow\left(3x-1\right)^2-4^2\)

\(\Leftrightarrow\left[\left(3x-1\right)+4\right]\left[\left(3x-1\right)-4\right]\)

\(\Leftrightarrow\left(3x-1+4\right)\left(3x-1-4\right)\)

\(\Leftrightarrow\left(3x+3\right)\left(3x-5\right)\)

\(\Leftrightarrow3\left(x+1\right)\left(3x-5\right)\)

   \(b.\left(5x-4\right)^2-49x^2\)

\(\Leftrightarrow\left(5x-4\right)^2-7^2x^2\)

\(\Leftrightarrow\left(5x-4\right)^2-\left(7x\right)^2\)

\(\Leftrightarrow\left[\left(5x-4\right)+7x\right]\left[\left(5x+4\right)-7x\right]\)

\(\Leftrightarrow\left(5x-4+7x\right)\left(5x+4-7x\right)\)

\(\Leftrightarrow\left(12x-4\right)\left(4-2x\right)\)

\(\Leftrightarrow4\left(3x-1\right)2\left(2-x\right)\)

\(\Leftrightarrow8\left(3x-1\right)\left(2-x\right)\)

   \(c.4x^2-\left(2x-4\right)^2\)

\(\Leftrightarrow2^2x^2-\left(2x-4\right)^2\)

\(\Leftrightarrow\left(2x\right)^2-\left(2x-4\right)^2\)

\(\Leftrightarrow\left[2x+\left(2x-4\right)\right]\left[2x-\left(2x-4\right)\right]\)

\(\Leftrightarrow\left(2x+2x-4\right)\left(2x-2x+4\right)\)

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

\(\Leftrightarrow4\left(x-1\right)4\)

\(\Leftrightarrow16\left(x-1\right)\)

   \(d.\left(3x-1\right)^2-4\left(x-2\right)^2\)

\(\Leftrightarrow\left(3x-1\right)^2-2^2\left(x-2\right)^2\)

\(\Leftrightarrow\left(3x-1\right)^2-\left[2\left(x-2\right)\right]^2\)

\(\Leftrightarrow\left[\left(3x-1\right)+2\left(x-2\right)\right]\left[\left(3x-1\right)-2\left(x-2\right)\right]\)

\(\Leftrightarrow\left(3x-1+2x-4\right)\left(3x-1-2x+4\right)\)

\(\Leftrightarrow\left(5x-5\right)\left(x+3\right)\)

\(\Leftrightarrow5\left(x-1\right)\left(x+3\right)\)

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

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

\(\Leftrightarrow\left(2x+3\right)^2-\left[2\left(2x+1\right)\right]^2\)

\(\Leftrightarrow\left[\left(2x+3\right)+2\left(2x+1\right)\right]\left[\left(2x+3\right)-2\left(2x+1\right)\right]\)

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

\(\Leftrightarrow\left(6x+5\right)\left(1-2x\right)\)

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

\(\Leftrightarrow\left[\left(2x+5\right)+\left(x-9\right)\right]\left[\left(2x+5\right)-\left(x-9\right)\right]\)

\(\Leftrightarrow\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)

\(\Leftrightarrow\left(3x-4\right)\left(x+14\right)\)

Bài 3

a) x² + 10x + 25

= x² + 2.x.5 + 5²

= (x + 5)²

b) 8x - 16 - x²

= -(x² - 8x + 16)

= -(x² - 2.x.4 + 4²)

= -(x - 4)²

c) x³ + 3x² + 3x + 1

= x³ + 3.x².1 + 3.x.1² + 1³

= (x + 1)³

d) (x + y)² - 9x²

= (x + y)² - (3x)²

= (x + y - 3x)(x + y + 3x)

= (y - 2x)(4x + y)

e) (x + 5)² - (2x - 1)²

= (x + 5 - 2x + 1)(x + 5 + 2x - 1)

= (6 - x)(3x + 4)

Bài 4

a) x² - 9 = 0

x² = 9

x = 3 hoặc x = -3

b) (x - 4)² - 36 = 0

(x - 4 - 6)(x - 4 + 6) = 0

(x - 10)(x + 2) = 0

x - 10 = 0 hoặc x + 2 = 0

*) x - 10 = 0

x = 10

*) x + 2 = 0

x = -2

Vậy x = -2; x = 10

c) x² - 10x = -25

x² - 10x + 25 = 0

(x - 5)² = 0

x - 5 = 0

x = 5

d) x² + 5x + 6 = 0

x² + 2x + 3x + 6 = 0

(x² + 2x) + (3x + 6) = 0

x(x + 2) + 3(x + 2) = 0

(x + 2)(x + 3) = 0

x + 2 = 0 hoặc x + 3 = 0

*) x + 2 = 0

x = -2

*) x + 3 = 0

x = -3

Vậy x = -3; x = -2

a, x^2 + 5x +4

= x^2 + 1x + 4x + 4

= (x^2 + 1x) + (4x + 4)

= x ( x + 1 ) + 4 ( x + 1 )

= (x + 1) (x + 4)

b, x^2 - 6x + 5

= x^2 - 1x - 5x + 5

= (x^2 - 1x) - (5x - 5)

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

= (x - 1) (x - 5)

c, x^2 + 7x + 12

= x^2 + 3x + 4x + 12 

= (x^2 + 3x) + (4x + 12)

= x (x + 3) + 4 (x + 3)

= (x + 3) (x + 4)

d, 2x^2 - 5x + 3

= 2^x2 - 2x - 3x + 3

= 2x (x - 1) - 3 (x - 1)

= (x-1) (2x - 3)

e, 7x  - 3x^2 - 4

= 3x + 4x - 3x^2 - 4

= (3x - 3x^2) + (4x - 4)

= 3x (1 - x) + 4 (x - 1)

= 3x (1-x) - 4 (1 - x)

= (1 - x) (3x - 4)

f, x^2 - 10x + 16

= x^2 - 2x - 8x + 16

= (x^2 - 2x) - (8x - 16)

= x (x - 2) - 8 (x - 2)

= (x - 2) (x - 8)

a, (x+1)(x+4)

b,(x-5)(x-1)

c,(x+3)(x+4)

d,(2x-3)(x-1)

e,(-3x+4)(x-1)

f, (x-8)(x-2)

\(a,\left(3x-1\right)^2-16=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\)

\(b,\left(5x-4\right)^2-49x^2=\left(12x-4\right)\left(-2x-4\right)=4\left(3x-1\right)\left(-2\right)\left(x+2\right)=-8\left(3x-1\right)\left(x+2\right)\)\(c,\left(2x+5\right)^2-\left(x-9\right)^2=\left(3x-4\right)\left(x+14\right)\)

a,\(\left(3x+1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\\ =\left(3x-17\right)\left(3x+15\right)\)

Dễ nhưng mà dài chết người 

Bài 1:

Ta có: \(x^2-2x+2=x^2-2x+1+1\)

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

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

Ta thấy rằng: \(\left(x-1\right)^2\ge0\) ( Với mọi \(x\in Z\) )

mà 1 > 0

=> \(\left(x-1\right)^2+1\ge0\)

<=> \(x^2-2x+1\ge0\)

Bài 3:

a) 53^2 + 47^2 + 94.53

= 53^2 + 47^2 + 2.47.53

= ( 53 + 47 )^2

= 100^2

= 10000

b) 50^2 - 49^2 + 48^2 - 47^2 + 2^2 - 1^2

= ( 50^2 - 49^2 ) + ( 48^2 - 47^2 ) + ( 2^2 - 1^2 )

= (50+49).(50-49) + (48+47).(48-47) + (2+1).(2-1)

= 50 + 49 + 48 + 47 + 2 + 1

= (49 + 1) + (48 + 2) + 50 + 47

= 50 + 50 + 50 + 47

= 197