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a) 3x^4 - 12x^2 = 3x^2.(x^2 - 4) = 3x^2.(x - 2)(x + 2)
b) x^2 - 2xy + 3x - 6y
= x(x - 2y) + 3(x - 2y)
= (x - 2y)(x + 3)
a) 3x^4 - 12x^2
= 3x^2.x^2- 3.4x^2
= x^2-4
b) x ^2 - 2xy + 3x - 6y
=(x^2-2xy) +(3x-6y)
=x.(x-2y)+3(x-2y)
=(x-2y).(x+3)
bạn ơi bạn viết sai đề có đề nào viết thế này đâu?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Trả lời:
a, x4 + 3x3 + x2 + 3x
= ( x4 + 3x3 ) + ( x2 + 3x )
= x3 ( x + 3 ) + x ( x + 3 )
= ( x3 + x ) ( x + 3 )
= x ( x2 + 1 ) ( x + 3 )
b, Sửa đề: x4 - x2 + 8x - 8
= ( x4 - x2 ) + ( 8x - 8 )
= x2 ( x2 - 1 ) + 8 ( x - 1 )
= x2 ( x - 1 ) ( x + 1 ) + 8 ( x - 1 )
= ( x - 1 ) [ x2 ( x + 1 ) + 8 ]
= ( x - 1 ) ( x3 + x2 + 8 )
Trả lời:
5, x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y ) ( x + 2 + y )
6, x2 + 2x - 4y2 - 4y
= ( x2 - 4y2 ) + ( 2x - 4y )
= ( x - 2y ) ( x + 2y ) + 2 ( x - 2y )
= ( x - 2y ) ( x + 2y + 2 )
7, 3x2 - 4y + 4x - 3y2
= ( 3x2 - 3y2 ) + ( 4x - 4y )
= 3 ( x2 - y2 ) + 4 ( x - y )
= 3 ( x - y ) ( x + y ) + 4 ( x - y )
= ( x - y ) [ 3 ( x + y ) + 4 ]
= ( x - y ) ( 3x + 3y + 4 )
8, x4 - 6x3 + 54x - 81
= ( x4 - 81 ) - ( 6x3 - 54x )
= ( x2 - 9 ) ( x2 + 9 ) - 6x ( x2 - 9 )
= ( x2 - 9 ) ( x2 + 9 - 6x )
= ( x - 3 ) ( x + 3 ) ( x - 3 )2
= ( x - 3 )3 ( x + 3 )
a, \(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
b, \(x^2+2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2+2y\right)\)
c, \(3x^2-4y+4x-3y^2=3\left(x-y\right)\left(x+y\right)-4\left(y-x\right)=\left(x-y\right)\left(3x+3y+4\right)\)
d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)
7, 4x mũ 2 - 12x + 9 - y mũ 2 = -(y-2x+3) (y+2x-3)
8, 16x mũ 2 - 4y mũ 2 + 4y - 1 = -(2y - 4x - 1) (2y+4x-1)
9, 25 - x mũ 2 - 12x - 36 = -(x+1) (x+11)
10, x mũ 2 - 9 - 5 ( x + 3 ) = (x-8) (x+3)
bạn k cho mình nha
chúc bạn học tốt :))))
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Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM
a, \(x^2-4-3\left(x-2\right)=\left(x-2\right)\left(x+2\right)-3\left(x-2\right)=\left(x-1\right)\left(x-2\right)\)
b, \(x^2-xy+5y-25=\left(x-5\right)\left(x+5\right)-y\left(x-5\right)=\left(x+5-y\right)\left(x-5\right)\)
c, \(x^3+x^2-2x-8=\left(x-2\right)\left(x^2+2x+4\right)+x\left(x-2\right)=\left(x-2\right)\left(x^2+3x+4\right)\)
d, \(x^3-4x^2-8x+8=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)=\left(x^2-6x+4\right)\left(x+2\right)\)
Trả lời:
1, x2 - 4 - 3 ( x - 2 )
= ( x2 - 4 ) - 3 ( x - 2 )
= ( x - 2 ) ( x + 2 ) - 3 ( x - 2 )
= ( x - 2 ) ( x + 2 - 3 )
= ( x - 2 ) ( x - 1 )
2, x2 - xy + 5y - 25
= ( x2 - 25 ) - ( xy - 5y )
= ( x - 5 ) ( x + 5 ) - y ( x - 5 )
= ( x - 5 ) ( x + 5 - y )
3, x3 + x2 - 2x - 8
= ( x3 - 8 ) + ( x2 - 2x )
= ( x - 2 ) ( x2 + 2x + 4 ) + x ( x - 2 )
= ( x - 2 ) ( x2 + 2x + 4 + x )
= ( x - 2 ) ( x2 + 3x + 4 )
4, x3 - 4x2 - 8x + 8
= ( x3 + 8 ) - ( 4x2 + 8x )
= ( x + 2 ) ( x2 - 2x + 4 ) - 4x ( x + 2 )
= ( x + 2 ) ( x2 - 2x + 4 - 4x )
= ( x + 2 ) ( x2 - 6x + 4 )
\(a)x^5+x^4+1\)
\(=x^3\left(x^2+x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x+1\right)\)
\(b)x^8+x^7+1\)
\(=\left(x^8-x^2\right)+\left(x^7-x\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
\(#Tuyết\)