(x² + x)² + 4x² + 4x - 12 (sửa đề)

= (x² + x)² + 4(x² + x) - 12

Đặt x² + x = y, ta có:

y² + 4y - 12

= y² + 2y - 6y - 12

= y(y + 2) - 6(y + 2)

= (y - 6)(y + 2)

= (x² + x - 6)(x² + x + 2)

= (x² - 2x + 3x - 6)(x² + x + 2)

= (x + 3)(x - 2)(x² + x + 2)

a) x³ - 4x² + 4x

= x(x² - 4x + 4)

= x(x - 2)²

b) x² - 3x + 2

= x² - x - 2x + 2

= (x² - x) + (2x - 2)

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

= (x + 2)(x - 1)

c) 8x³ + \(\dfrac{1}{27}\)

= \(\left(2x+\dfrac{1}{3}\right)\)\(\left(4x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)\)

d) 64x³ - \(\dfrac{1}{8}\)

= \(\left(4x+\dfrac{1}{2}\right)\left(16x^2-2x+\dfrac{1}{4}\right)\)

e) x² - 4 + (x - 2)²

= (x + 2)(x - 2) - (x - 2)²

= (x - 2)[(x + 2) - (x - 2)]

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

= 4(x - 2)

f) x³ - 2x³ + x - xy²

= -x³ + x - xy²

= -x(x² - 1 + y²)

g) x³ - 4x² - 12x + 27

= (x³ + 27) - (4x² + 12x)

= (x + 3)(x² - 3x + 9) - 4x(x + 3)

= (x + 3)[(x² - 3x + 9) - 4x]

= (x + 3)(x² - 3x + 9 - 4x)

= (x + 3)(x² - 7x + 9)

h) 2x - 2y - x² + 2xy - y²

= (2x - 2y) - (x² - 2xy + y²)

= 2(x - y) - (x - y)²

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

i) 3x² + 6x + 3 - 3y²

⁼ 3(x² + 2x + 1 - y²)

= 3[(x² + 2x + 1) - y²]

= 3[(x + 1)² - y²]

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

k) 25 - x² - y² + 2xy

= 25 - (x² - 2xy + y²)

= 25 - (x - y)²

= (5 - x + y)(5 + x - y)

l) 3x - 3y - x² + 2xy - y²

= (3x - 3y) - (x² - 2xy + y²)

= 3(x - y) - (x - y)²

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

m) x² - y² + 2x - 2y

= (x² - y²) + (2x - 2y)

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

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

n) x⁴ + 2x³ - 4x - 4

= (x⁴ - 4) + (2x³ - 4x)

= (x² - 2)(x² + 2) + 2x(x² - 2)

= (x² - 2)(x² + 2 + 2x)

o) x²(1 - x²) - 4x - 4x²

= x²(1 - x)( 1 + x) - 4x(1 + x)

= x(1 + x)[x(1 - x) - 4x]

= x(x + 1)(x - x² - 4)

p) x³ + y³ + z³ - 3xyz

= x³ + y³ + z³ - 3x²y + 3x²y - 3xy² + 3xy² - 3xyz

= [(x³ + 3x²y + 3xy² + y³) + z³] - (3x²y + 3xy² + 3xyz)

= [(x + y)³ + z³] - 3xy(x + y + z)

= (x + y + z)[(x + y)² - (x + y)z + z²] - 3xy(x + y + z)

= (x + y + z)(x² + 2xy + y² - xz - yz + z² - 3xy)

= (x + y + z)(x² + y² + z² - xy - xz - yz)

q) (x - y)³ + (y - z)³ + (z - x)³

= [(x - y) + (y - z)][(x - y)² - (x - y)(y - z) + (y - z)²] + (z - x)³

= (x - z)(x² - 2xy + y² - xy + xz - y² + yz + y² - 2yz + z²) - (x - z)³

= (x - z)(x² + y² + z² - 3xy + xz - yz) - (x - z)³

= (x - z)[x² + y² + z² - 3xy + xz - yz - (x - z)²]

= (x - z)(x² + y² - 3xy + xz - yz - x² + 2xz - z²)

= (x - z)(y² - 3xy + 3xz - yz)

= (x - z)[(y² - yz) - (3xy - 3xz)]

= (x - z)[y(y - z) - 3x(y - z)

= (x - z)(y - 3x)(y - z)

Nhớ tik nha

Tìm x:

8x² - (2x + 5)(4x - 2) - 9 = 0

8x² - (8x² - 4x + 20x - 10) - 9 = 0

8x² - 8x² +4x - 20x + 10 - 9 = 0

-16x + 1 = 0

=> -16x = -1

=> x = \(\dfrac{1}{16}\)

Phân tích Đa thức thành nhân tử:

con a bn xem lại đi nhé

mạn phép chữa đề:

b) 3x² - 6xy + 3y² - 12z²

= 3(x² - 2xy + y² - 4z²)

= 3[(x² - 2xy + y²) - 4z²]

= 3[(x - y)² - 4z²]

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

c) x² - 3x + 2

C1:

x² - 3x + 2

= x² - 3x - 1 + 3

= (x² - 1) - (3x - 3)

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

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

=(x - 1)(x - 2)

C2: x² - 3x + 2

= 3x² - 2x² - 3x + 2

= (3x² - 3x) - (2x² - 2)

= 3x(x - 1) - 2(x² - 1)

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

= (x - 1)[3x - 2(x + 1)]

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

= (x - 1)(x - 2)

C3: x² - 3x + 2

= x² - x - 2x + 2

= (x² - x) - (2x - 2)

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

= (x - 2)(x - 1)

Chúc Bn Hok Tốt

\(\)

Nhớ tik nha ko lần sau mk ko giúp đâu

số chia hết cho 3 và 7 thì chia hết cho 21 gồm

105;126;......;966;987

có : ( 987 - 105) : 21 + 1 = 43

số có 3 chữ số chia hết cho 3 mà ko chia hết cho 7 là 300 - 43 = 257 số

nhớ ****