Phân tich đa Thức thành nhân tử.
a,3xy +5xy mũ 2-xy mũ 2
b,x(y-x)+3(y-x)
Phân tích đa thức thành nhân tử
a,-3xy mũ 2+ x mũ 2y mũ 2-5x mũ 2y
b,x mũ 2(x+1)-(x+1)
C, y mũ 2+ xy+ y
d,4x(x-2)-(x-2)
,
b)x2(x+1)-(x+1)=(x+1)(x2-1)
d) 4x(x-2)-(x-2)=(x-2)(4x-1)
câu a bn ghi mik k hỉu
bài 2; phân tích đa thức sau thành nhân tử
a, x mũ 2 + 7x + 7y - y mũ 2
b, x mũ 2 - 2x - 9y mũ 2 + 6y
c, x mũ 2 - xy +x mũ 3 - 3x mũ 2 y + 3x mũ 2 y - y mũ 3
\(a,x^2+7x+7y-y^2\)
\(=x^2-y^2+7\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(b,x^2-2x-9y^2+6y\)
\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)
bài 1; phân tích các đa thức sau thành nhân tử
a, x mũ 2 - xy - x + y
b, xy + 4 - x mũ 2 + 2y
c, xy + y - 2 ( x + 1 )
d, 5(x - y )+ ax - ay
a)x2-xy-x+y
=(x2-x)-(xy-y)
=x(x-1)-y(x-1)
=(x-1)(x-y)
b) xy+4-x2+2y
=(4-x2)+(xy+2y)
=(2-x)(x+2)+y(x+2)
=(x+2)(2-x+y)
c) xy+y-2(x+1)
=y(x+1)-2(x+1)
=(x+1)(y-2)
d) 5(x-y)+ax-ay
=5(x-y)+a(x-y)
=(x-y)(5+a)
#H
Trả lời:
a, x2 - xy - x + y
= ( x2 - xy ) - ( x - y )
= x ( x - y ) - ( x - y )
= ( x - y ) ( x - 1 )
b, xy + 4 - x2 + 2y
= ( xy + 2y ) - ( x2 - 4 )
= y ( x + 2 ) - ( x - 2 ) ( x + 2 )
= ( x + 2 ) ( y - x + 2 )
c, xy + y - 2 ( x + 1 )
= y ( x + 1 ) - 2 ( x + 1 )
= ( x + 1 ) ( y - 2 )
d, 5 ( x - y ) + ax - ay
= 5 ( x - y ) + a ( x - y )
= ( 5 + a ) ( x - y )
a) \(x^2-xy-x+y=\left(x^2-x\right)-\left(xy-y\right)=x\left(x-1\right)-y\left(x-1\right)=\left(x-1\right)\left(x-y\right)\)
b)\(xy+4-x^2+2y=\left(xy+2y\right)+\left(4-x^2\right)=y\left(x+2\right)+\left(2-x\right)\left(2+x\right)=\left(x+2\right)\left(y+2-x\right)\)
c) \(xy+y-2\left(x+1\right)=\left(xy+y\right)-2\left(x+1\right)=y\left(x+1\right)-2\left(x+1\right)=\left(x+1\right)\left(y-2\right)\)
d)\(5\left(x-y\right)+ax-ay=5\left(x-y\right)+\left(ax-ay\right)=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)
phân tích đa thức sau thành nhân tử
t, x mũ 2 y - xy mũ 2 + x mũ 3 - y mũ 3
o, 4x mũ 2 - 25 + ( 2x + 7 )( 5 - 2x )
p, 5x mũ 2 - 5y mũ 2 - 10x + 10y
r, x mũ 2 - xy + 4x - 2y + 4
a)x²−2x−4y²−4ya)x²-2x-4y²-4y
=x²−2x−4y²−4y+2xy−2xy=x²-2x-4y²-4y+2xy-2xy
=(x²−2xy−2x)+(2xy−4y²−4y)=(x²-2xy-2x)+(2xy-4y²-4y)
=x(x−2y−2)+2y(x−2y−2)=x(x-2y-2)+2y(x-2y-2)
=(x+2y)(x−2y−2)=(x+2y)(x-2y-2)
b)x4+2x³−4x−4b)x4+2x³-4x-4
=x4+2x³+2x²−2x²−4x−4=x4+2x³+2x²-2x²-4x-4
=(x4+2x³+2x²)−(2x²+4x+4)=(x4+2x³+2x²)-(2x²+4x+4)
=x²(x²+2x+2)−2(x²+2x+2)=x²(x²+2x+2)-2(x²+2x+2)
=(x²−2)(x²+2x+2)=(x²-2)(x²+2x+2)
c)x³+2x²y−x−2yc)x³+2x²y-x-2y
=x²(x+2y)−(x+2y)=x²(x+2y)-(x+2y)
=(x²−1)(x+2y)=(x²-1)(x+2y)
=(x+1)(x−1)(x+2y)=(x+1)(x-1)(x+2y)
d)3x²−3y²−2(x−y)²d)3x²-3y²-2(x-y)²
=3(x²−y²)−2(x−y)²=3(x²-y²)-2(x-y)²
=3(x+y)(x−y)−2(x−y)²=3(x+y)(x-y)-2(x-y)²
=(x−y)[3(x+y)−2(x−y)]=(x-y)[3(x+y)-2(x-y)]
=(x−y)(3x+3y−2x+2y)=(x-y)(3x+3y-2x+2y)
=(x−y)(x+5y)=(x-y)(x+5y)
e)x³−4x²−9x+36e)x³-4x²-9x+36
=(x³−4x²)−(9x−36)=(x³-4x²)-(9x-36)
=x²(x−4)−9(x−4)=x²(x-4)-9(x-4)
=(x−4)(x²−9)=(x-4)(x²-9)
=(x−4)(x²−3²)=(x-4)(x²-3²)
=(x−4)(x+3)(x−3)=(x-4)(x+3)(x-3)
f)x²−y²−2x−2yf)x²-y²-2x-2y
=(x²−y²)−(2x+2y)=(x²-y²)-(2x+2y)
=(x+y)(x−y)−2(x+y)=(x+y)(x-y)-2(x+y)
=(x+y)(x−y−2)
hok tốt nhé
k đi
bài 2; phân tích các đa thức sau thành nhân tử
a, x mũ 2 + 4x - y mũ 2 + 4
b, 25 - 4x mũ 2 - 4xy - y mũ 2
c, x mũ 3 - x + y mũ 3 - y
\(a,x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
\(b,25-4x^2-4xy-y^2\)
\(=25-\left(4x^2+4xy+y^2\right)\)
\(=5^2-\left(2x+y\right)^2\)
\(=\left(5-2x+y\right)\left(5+2x+y\right)\)
\(c,x^3-x+y^3-y\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+1\right)\)
phân tích đa thức sau thành nhân tử
11, 5( x - y ) + y mũ 2 - xy
12, 14a mũ 2 b mũ 3 - 35ab mũ 2 + 7a mũ 2 b mũ 2
13, 6a mũ 2 b mũ 3 - 30ab mũ 2 + 12a mũ 2 b
11, \(5\left(x-y\right)+y^2-xy=5\left(x-y\right)+y\left(y-x\right)=\left(5-y\right)\left(x-y\right)\)
12, \(14a^2b^3-35ab^2+7a^2b^2=7ab^2\left(2ab-5+a\right)\)
13, \(6a^2b^3-30ab^2+12a^2b=6ab\left(ab^2-5b+2a\right)\)
phân tích đa thức sau thành nhân tử
11, 5 ( x - y ) + y mũ 2 - xy
12, 14a mũ 2 b mũ 3 - 35ab mũ 2 + 7a mũ 2 b mũ 2
13, 6a mũ 2 b mũ 3 - 30 ab mũ 2 + 12a mũ 2 b
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Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM
bài 2 ; phân tích các đa thưucs sau thành nhân tử
g, 5x mũ 2 - 5xy + 7y + 7x
h, x mũ y - xz + z -y
i, x mũ 3 + 2x mũ 2 - 3x -6
g, sửa đề
\(5x^2-5xy+7y-7x=5x\left(x-y\right)+7\left(y-x\right)=\left(5x-7\right)\left(x-y\right)\)
h, sửa đề
\(xy-xz+z-y=x\left(y-z\right)-\left(y-z\right)=\left(x-1\right)\left(y-z\right)\)
i, \(x^3+2x^2-3x-6=x^2\left(x+2\right)-3\left(x+2\right)=\left(x^2-3\right)\left(x+2\right)\)
bài 1; phân tích các đa thức sau thành nhân tử
1, x mũ 2( x - 3 )- 4x + 12
2, 2a(x + y) - x - y
3, 2x - 4 + 5x mũ 2 - 10x
4, 5x mũ 2 - 12x - 7x + 14
5, xy - y mũ 2 - 3x + 3y
1, \(x^2\left(x-3\right)-4x+12=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)
2, \(2a\left(x+y\right)-x-y=2a\left(x+y\right)-\left(x+y\right)=\left(2a-1\right)\left(x+y\right)\)
3, \(2x-4+5x^2-10x=2\left(x-2\right)+5x\left(x-2\right)=\left(2+5x\right)\left(x-2\right)\)
4, sửa đề :
\(6x^2-12x-7x+14=6x\left(x-2\right)-7\left(x-2\right)=\left(6x-7\right)\left(x-2\right)\)
5, \(xy-y^2-3x+3y=y\left(x-y\right)-3\left(x-y\right)=\left(y-3\right)\left(x-y\right)\)
a) x2(x-3)-4x+12
=x2(x-3)-4(x-3)
=(x-3)(x2-4)
=(x-3)(x-2)(x+2)
b) 2a(x+y)-x-y
=2a(x+y)-(x+y)
=(x+y)(2a-1)
c) 2x-4+5x2-10x
=2(x-2)+5x(x-2)
=(x-2)(2+5x)
d) 5x2-12x-7x+14
=5x2-19x+14
e) xy-y2-3x+3y
=y(x-y)-3(x-y)
=(x-y)(y-3)
#H
Trả lời:
1, x2 ( x - 3 ) - 4x + 12 = x2 ( x - 3 ) - 4 ( x - 3 ) = ( x - 3 )( x2 - 4 ) = ( x - 3 )( x - 2 )( x + 2 )
2, 2a ( x + y ) - x - y = 2a ( x + y ) - ( x + y ) = ( x + y )( 2a - 1 )
3, 2x - 4 + 5x2 - 10x = ( 2x - 4 ) + ( 5x2 - 10x ) = 2 ( x - 2 ) + 5x ( x - 2 ) = ( x - 2 )( 2 + 5x )
4, Sửa đề: 6x2 - 12x - 7x + 14 = ( 6x2 - 12x ) - ( 7x - 14 ) = 6x ( x - 2 ) - 7 ( x - 2 ) = ( x - 2 )( 6x - 7 )
5, xy - y2 - 3x + 3y = ( xy - y2 ) - ( 3x - 3y ) = y ( x - y ) - 3 ( x - y ) = ( x + y )( y - 3 )