A=(x+1)(x+2)(x+3)(x+4)=(x+1)(x+4)(x+2)(x+3)=(x^2+5x+4)(x^2+5x+6)

Đặt x^2+5x=t =>A=(t+4)(t+6)=t^2+10t+24=(t+5)^2-1 lớn hơn hoặc bằng -1 

Dấu bằng xảy ra khi t=-5 từ đó giải ra x

mik chỉ nghĩ đc cái này thôi

(x+1)(x+2)(x+3)(x+4)

mơn bn nhennnn

Lưu ý : dấu " : " là dấu " chia hết cho "

a) 

2a + b : 13

=> 2 ( 2a + b ) : 13

=> 4a + 2b : 13

mà 5a - 4b : 13

=> 5a - 4b - 4a - 2b : 13

=> a - 6b : 13 ( đpcm )

b)

Đặt A = 100a + b và B = a + 4b

Vì A : 7

=> 3A : 7

hay 300a + 3b : 7

Xét 3A + B

= 300a + 3b + a + 4b

= 301a + 7b

= 7 ( 43a + b ) : 7

=> 3A + B : 7

mà 3A : 7 ( cm trên ) => B : 7 hay a + ab : 7 ( đpcm )

\(a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\))

\(=a^3\left(b-c\right)-b^3\left(a-c\right)+c^3\left(a-b\right)\)

\(=a^3\left(b-c\right)-b^3\left[\left(b-c\right)+\left(a-b\right)\right]+c^3\left(a-b\right)\)

\(=a^3\left(b-c\right)-b^3\left(b-c\right)-b^3\left(a-b\right)+c^3\left(a-b\right)\)

\(=\left(b-c\right)\left(a^3-b^3\right)-\left(a-b\right)\left(b^3-c^3\right)\)

\(=\left(b-c\right)\left(a-b\right)\left(a^2+ab+b^2\right)-\left(a-b\right)\left(b-c\right)\left(b^2+bc+c^2\right)\)

\(=\left(a-b\right)\left(b-c\right)\left[\left(a^2+ab+b^2\right)-\left(b^2+bc+c^2\right)\right]\)

\(=\left(a-b\right)\left(b-c\right)\left(a^2-c^2+ab-bc\right)\)

\(=\left(a-b\right)\left(b-c\right)\left[\left(a-c\right)\left(a+c\right)+b\left(a-c\right)\right]\)

\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\left(a+b+c\right)\)

= x ³ + y ³ + z³ - x³ - y³ - z³

\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

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

\(=\left(x+y\right)^3+3\left(x+y\right)z\left(x+y+z\right)+z^3-x^3-y^3-z^3\)

\(=3xy\left(x+y\right)+3\left(x+y\right)z\left(x+y+z\right)\)

\(=3\left(x+y\right)\left(xy+xz+yz+z^2\right)\)

\(=3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)

\(=3\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

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

a) x³   + 3x² + 3x + 1

= x³ + 3.x².1 + 3.x.1² + 1³

= (x+1)³