thiếu đề bài 

PTTNT ă bạn

a) (x+y)³-(x-y)³

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

 rùi nhé!! 564576578768797809678458426546456457657426

(x + y)³ - (x - y)³

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

nãy làm lộn!! 45746746356545645646464562452524534645765776345245646

\(x^2+4xy+4y^2-4z^2-1-4z\)

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

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

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

= ( x² + 4xy +4y² ) - ( 4z² +4z +1 ) 
= ( x + y )² - [ (2z)² - 2z.1 +1²)]
= ( x + y )²  - (2z+1)²
= ( x + y - 2z - 1 ).( x + y + 2z + 1 )
 

=\(x^2+2.x.2y+\left(2y\right)^2-\left[\left(2z\right)^2+2.2z.1+1^2\right]=\left(x+2y\right)^2-\left(2z+1\right)^2=\left(x+2y+2z+1\right)\left(x+2y-2z-1\right)\)

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

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

= (x²+5x+4)(x²+5x+6)

=(x²+5x+4)²+2(x²+5x+4)+1-1

= (x²+5x+5)²-1

Vì (x²+5x+5)² luôn lớn hơn hoặc bằng 0 với mọi x=> (x²+5x+5)²-1 luôn lớn hơn hoặc bằng -1 với mọi x

=> GTNN của (x+1)(x+2)(x+3)(x+4) là -1 khi và chỉ khi x = \(\sqrt{1,25}\)-2,5 hoặc x = - (2,5+\(\sqrt{1,25}\))
 

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

\(=x.\left(x+2\right)+1.\left(x+2\right)+x.\left(x+3\right)+1.\left(x+3\right)+x.\left(x+4\right)+1.\left(x+4\right)\)

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

\(=3x^2+12x+9\)

Vậy GTNN là 9

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

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

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

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

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

\(C=x^4-x^3-x+1=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)

Đoàn Thị Huyền Đoan: Hình như câu A bạn chép xuống bị sai đề rồi!

tính gì vậy bạn?

(5n-2)²-4=(5n-2-2)(5n-2+2)=(5n-4).5n chia hết cho 5

=>dpcm

\(\left(5n-2\right)^2-4=25n^2-20n+4-4=25n^2-20n=5n\left(5n-4\right)\)chia hết cho 5.

Vậy (5n2 -2)² -4 chia hết cho 5 (đpcm)