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a) x ( x +1 ) 2 + ( x - 5 ) - 5( x +1 )2
=( x +1 )2.(x-5)2
=( (x +1)+(x-5)).((x +1)-(x-5))
a) x ( x +1 ) 2 + ( x - 5 ) - 5( x +1 )2
= ( x + 1 )2 ( x - 5 ) + ( x - 5 )
= ( x - 5 ) ( x2 + 2x + 1 +1 )
= ( x - 5 ) ( x2 + 2x + 2 )
b) 3x2 - 12y2
= 3 ( x2 - 4y2 )
= 3 ( x -2y ) (x + 2y )
c) x3 + 3x2 + 3x +1 - 27z3
= ( x + 1 )3 - (3z )3
= ( x + 1 - 3z ) [ ( x + 1 )2 + 3z ( x + 1 ) +9z2 ]
= ( x + 1 - 3z) [( x + 1 ) 2 + 3xz + 3z + 9z2 ]
Bài 1 :
\(=\left(x^3-x\right)-\left(6x+6\right)\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x+1\right)\left(x-1\right)-6\left(x+1\right)\)
\(=\left(x^2-x\right)\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x^2-x-6\right)\left(x+1\right)\)
b: \(=ab^2+ac^2+abc+bc^2+ba^2+abc+a^2c+b^2c+abc\)
\(=ab\left(a+b+c\right)+bc\left(a+b+c\right)+ac\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(ab+bc+ac\right)\)
a: \(=\left(x^2-x^2y^2\right)+\left(y^2-y\right)+\left(xy-x\right)\)
\(=-x^2\left(y-1\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=\left(y-1\right)\left(-x^2y-x^2+y+x\right)\)
\(=\left(1-y\right)\left(x^2y+x^2-x-y\right)\)
\(=\left(1-y\right)\cdot\left[y\left(x-1\right)\left(x+1\right)+x\left(x-1\right)\right]\)
\(=\left(1-y\right)\left(x-1\right)\left(xy+y+x\right)\)
Câu a) dễ, ko làm
b) \(x^2y^2+1-x^2-y^2\)
\(=x^2\left(y^2-1\right)-\left(y^2-1\right)\)
\(=\left(x^2-1\right)\left(y^2-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(y+1\right)\left(y-1\right)\)
Câu c) đề sai
Câu c) ,đề đúng nek
\(bc\left(b+c\right)+ac\left(c-a\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left[\left(b+c\right)-\left(a+b\right)\right]-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left(b+c\right)-ac\left(a+b\right)-ab\left(a+b\right)\)
\(=\left(b+c\right)\left(bc+ac\right)-\left(a+b\right)\left(ac+ab\right)\)
\(=\left(b+c\right)c\left(a+b\right)-\left(a+b\right)a\left(b+c\right)\)
\(=\left(b+c\right)\left(a+b\right)\left(c-a\right)\)
Bài 2:
a) \(A=ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)
\(=\left(a-b\right)\left(c-a\right)\left(c-b\right)\)
b) \(B=a\left(b^2-c^2\right)+b^2\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)
\(=\left(b-a\right)\left(c-a\right)\left(c-b\right)\)
c) \(C=\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=3\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
p/s: từ sau bn đăng 1-2 bài thôi nhé, nhiều thế này người lm bài cx hơi bất tiện để đọc đề
còn mấy câu nữa bn đăng lại nhé
Đăng từng bài thui bn êi ~.~
\(h)\)\(\left(xy+1\right)^2-\left(x+y\right)^2\)
\(=\)\(\left(xy-x-y+1\right)\left(xy+x+y+1\right)\)
\(=\)\(\left[x\left(y-1\right)-\left(y-1\right)\right].\left[x\left(y+1\right)+\left(y+1\right)\right]\)
\(=\)\(\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)\)
\(i)\)\(16b^2c^2-4\left(b^2+c^2-a^2\right)^2\)
\(=\)\(\left(4bc\right)^2-\left(2b^2+2c^2-2a^2\right)^2\)
\(=\)\(\left(4bc-2b^2-2c^2+2a^2\right)\left(4bc+2b^2+2c^2-2a^2\right)\)
\(=\)\(2\left[a^2-\left(b^2-2bc+c^2\right)\right].2\left[\left(b^2+2bc+c^2\right)-a^2\right]\)
\(=\)\(-4\left[a^2-\left(b-c\right)^2\right].\left[a^2-\left(b+c\right)^2\right]\)
\(=\)\(-4\left(a-b+c\right)\left(a+b-c\right)\left(a-b-c\right)\left(a+b+c\right)\)
Chúc bạn học tốt ~
Lười ._. Đăng luôn zợ cho nhanh =^=