x3 - 3x2 + 1 - 3x
x2 - 6xy - 25z2 + 9y2
x2 - y2 - x - y
x2 - y2 + 4 - 4x
a3 - ay - a2 x + xy
Những câu hỏi liên quan
Bài 1: Rút gọn các biểu thức:a. (2x - 1)2 - 2(2x - 3)2 + 4 b. (3x + 2)2 + 2(2 + 3x)(1 - 2y) + (2y - 1)2 c. (x2 + 2xy)2 + 2(x2 + 2xy)y2 + y4 d. (x - 1)3 + 3x(x - 1)2 + 3x2(x -1) + x3 e. (2x + 3y)(4x2 - 6xy + 9y2) f. (x - y)(x2 + xy + y2) - (x + y)(x2 - xy + y2) g. (x2 - 2y)(x4 + 2x2y + 4y2) - x3(x – y)(x2 + xy + y2) + 8y3
Đọc tiếp
Bài 1: Rút gọn các biểu thức:
a. (2x - 1)2 - 2(2x - 3)2 + 4
b. (3x + 2)2 + 2(2 + 3x)(1 - 2y) + (2y - 1)2
c. (x2 + 2xy)2 + 2(x2 + 2xy)y2 + y4
d. (x - 1)3 + 3x(x - 1)2 + 3x2(x -1) + x3
e. (2x + 3y)(4x2 - 6xy + 9y2)
f. (x - y)(x2 + xy + y2) - (x + y)(x2 - xy + y2)
g. (x2 - 2y)(x4 + 2x2y + 4y2) - x3(x – y)(x2 + xy + y2) + 8y3
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
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Bài 1: Rút gọn các biểu thức:a. (2x - 1)2 - 2 (2x - 3)2 + 4 b. (3x + 2)2 + 2 (2 + 3x) (1 - 2y) + (2y - 1)2 c. (x2 + 2xy)2 + 2 (x2 + 2xy) y2 + y4 d. (x - 1)3 + 3x (x - 1)2 + 3x2 (x -1) + x3 e. (2x + 3y) (4x2 - 6xy + 9y2) f. (x - y) (x2 + xy + y2) - (x + y) (x2 - xy + y2) g. (x2 - 2y) (x4 + 2x2y + 4y2) - x3 (x – y) (x2 + xy + y2) + 8y3
Đọc tiếp
Bài 1: Rút gọn các biểu thức:
a. (2x - 1)2 - 2 (2x - 3)2 + 4
b. (3x + 2)2 + 2 (2 + 3x) (1 - 2y) + (2y - 1)2
c. (x2 + 2xy)2 + 2 (x2 + 2xy) y2 + y4
d. (x - 1)3 + 3x (x - 1)2 + 3x2 (x -1) + x3
e. (2x + 3y) (4x2 - 6xy + 9y2)
f. (x - y) (x2 + xy + y2) - (x + y) (x2 - xy + y2)
g. (x2 - 2y) (x4 + 2x2y + 4y2) - x3 (x – y) (x2 + xy + y2) + 8y3
a: Ta có: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
b: \(\left(3x+2\right)^2+2\left(3x+2\right)\left(1-2y\right)+\left(1-2y\right)^2\)
\(=\left(3x+2+1-2y\right)^2\)
\(=\left(3x-2y+3\right)^2\)
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phân tích đa thức thành nhân tử
a) xy+y2-x-y
b) 25-x2+4xy-4y2
c) xy+yz-2y-2z
d) x2-6xy+9y2-25z2
e) 3x2-3y2-12x+12y
f) 4x3+4xy2+8x2y-16x
g) x2-5x+4
h) x4+5x2+4
i) 2x2+3x-5
k) x3-2x2+6x-5
l) x2-4x+3
Mong mọi người giúp đỡ em cảm ơn ạ
Bài làm
a) xy + y2 - x - y
= ( xy + y2 ) - ( x + y )
= y( x + y ) - ( x + y )
= ( x + y )( y - 1 )
b) 25 - x2 + 4xy - 4y2
= 25 - ( x2 - 4xy + 4y2 )
= 25 - ( x - 2y )2
= ( 5 - x + 2y )( 5 + x - 2y )
c) xy + xz - 2y - 2z
= ( xy + xz ) - ( 2y + 2z )
= x( y + z ) - 2( y + z )
= ( y + z )( x - 2 )
d) x2 - 6xy + 9y2 - 25z2
= ( x2 - 6xy + 9y2 ) - 25z2
= ( x - 3y )2 - 25z2
= ( x - 3y - 5z )( z - 3y + 5z )
e) 3x2 - 3y2 - 12x + 12y
= 3( x - y )( x + y ) - 12( x - y )
= ( x - y )[ 3( x + y ) - 12 ]
f) 4x3 + 4xy2 + 8x2y - 16x
= 4x( x2 + y2 + 2xy - 4 )
= 4x[ ( x + y)2 - 4 ]
= 4x( x + y - 2 )( x + y + 2 )
g) x2 - 5x + 4
= x2 - x - 4x + 4
= x( x - 1 ) - 4( x - 1 )
= ( x - 1 )( x - 4 )
h) x4 + 5x2 + 4
= x4 + x2 + 4x2 + 4
= x2( x2 + 1 ) + 4( x2 + 1 )
= ( x2 + 1 )( x2 + 4 )
i) 2x2 + 3x - 5
= 2x2 - 5x + 2x - 5
= 2x( x + 1 ) - 5( x + 1 )
= ( x + 1 )( 2x - 5 )
k) x3 - 2x2 + 6x - 5 ( không biết làm )
l) x2 - 4x + 3
= ( x2 - 4x + 4 ) - 1
= ( x - 2 )2 - 1
= ( x - 3 )( x - 1 )
# Học tốt #
1) x3-x2+2x-2 4) ax-2x-a2+2a 7) x2-6xy-25z2+9y2
2) x2-y2+2x+2y 5) 2xy +3z+6y+xz 8) x3-2x2+x
3) x2/4+2xy+4y2-25 6) x2y2+yz+y3+zx2 9) x4+4
6). – x2 y(xy2 – 1/2 xy + 3/4 x2 y2 )7). (3xy – x2 + y). 2/3 x2 y8). (4x3 – 5xy + 2x)( – 1/2 xy)9). 2x2 (x2 + 3x + 1/2 )10). – 3/2 x4 y2 (6x4 − 10/9 x2 y3 – y5 )11). 2 3 x3 (x + x2 – 3/4 x5 )12). 2xy2 (xy + 3x2 y – 2/3 xy3 )13). 3x(2x3 – 1/3 x2 – 4x)14). 3/5 x3 y5 (7x4 + 5x2 y − 10/21 x4 y3 –y4 )
Đọc tiếp
6). – x2 y(xy2 – 1/2 xy + 3/4 x2 y2 )
7). (3xy – x2 + y). 2/3 x2 y
8). (4x3 – 5xy + 2x)( – 1/2 xy)
9). 2x2 (x2 + 3x + 1/2 )
10). – 3/2 x4 y2 (6x4 − 10/9 x2 y3 – y5 )
11). 2 3 x3 (x + x2 – 3/4 x5 )
12). 2xy2 (xy + 3x2 y – 2/3 xy3 )
13). 3x(2x3 – 1/3 x2 – 4x)
14). 3/5 x3 y5 (7x4 + 5x2 y − 10/21 x4 y3 –y4 )
6: \(-x^2y\left(xy^2-\dfrac{1}{2}xy+\dfrac{3}{4}x^2y^2\right)\)
\(=-x^3y^3+\dfrac{1}{2}x^3y^2-\dfrac{3}{4}x^4y^3\)
7: \(\dfrac{2}{3}x^2y\cdot\left(3xy-x^2+y\right)\)
\(=2x^3y^2-\dfrac{2}{3}x^4y+\dfrac{2}{3}x^2y^2\)
8: \(-\dfrac{1}{2}xy\left(4x^3-5xy+2x\right)\)
\(=-2x^4y+\dfrac{5}{2}x^2y^2-x^2y\)
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9: \(2x^2\left(x^2+3x+\dfrac{1}{2}\right)=2x^4+6x^3+x^2\)
10: \(-\dfrac{3}{2}x^4y^2\left(6x^4-\dfrac{10}{9}x^2y^3-y^5\right)\)
\(=-9x^8y^2+\dfrac{5}{3}x^6y^5+\dfrac{3}{2}x^4y^7\)
11: \(\dfrac{2}{3}x^3\left(x+x^2-\dfrac{3}{4}x^5\right)=\dfrac{2}{3}x^3+\dfrac{2}{3}x^5-\dfrac{1}{2}x^8\)
12: \(2xy^2\left(xy+3x^2y-\dfrac{2}{3}xy^3\right)=2x^2y^3+6x^3y^3-\dfrac{4}{3}x^2y^5\)
13: \(3x\left(2x^3-\dfrac{1}{3}x^2-4x\right)=6x^4-x^3-12x^2\)
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10) x(x-y)+x2-y2
11) x2 -y2 +10x-10y
12) x2-y2 +20x+20y
13) 4x2 -9y2-4x-6y
14) x3-y3+7x2-7y2
15) x3+4x-(y3+4y)
16) x3+y3+2x+2y
17) x3-y3-2x2y+2xy2
18) x3-4x2+4x-xy2
10: \(x\left(x-y\right)+x^2-y^2\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x+x+y\right)\)
\(=\left(x-y\right)\left(2x+y\right)\)
11: \(x^2-y^2+10x-10y\)
\(=\left(x^2-y^2\right)+\left(10x-10y\right)\)
\(=\left(x-y\right)\left(x+y\right)+10\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+10\right)\)
12: \(x^2-y^2+20x+20y\)
\(=\left(x^2-y^2\right)+\left(20x+20y\right)\)
\(=\left(x-y\right)\left(x+y\right)+20\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+20\right)\)
13: \(4x^2-9y^2-4x-6y\)
\(=\left(4x^2-9y^2\right)-\left(4x+6y\right)\)
\(=\left(2x-3y\right)\left(2x+3y\right)-2\left(2x+3y\right)\)
\(=\left(2x+3y\right)\left(2x-3y-2\right)\)
14: \(x^3-y^3+7x^2-7y^2\)
\(=\left(x^3-y^3\right)+\left(7x^2-7y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+7\cdot\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+7\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+7x+7y\right)\)
15: \(x^3+4x-\left(y^3+4y\right)\)
\(=x^3-y^3+4x-4y\)
\(=\left(x^3-y^3\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+4\right)\)
16: \(x^3+y^3+2x+2y\)
\(=\left(x^3+y^3\right)+\left(2x+2y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+2\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+2\right)\)
17: \(x^3-y^3-2x^2y+2xy^2\)
\(=\left(x^3-y^3\right)-\left(2x^2y-2xy^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)-2xy\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2-2xy\right)\)
\(=\left(x-y\right)\left(x^2-xy+y^2\right)\)
18: \(x^3-4x^2+4x-xy^2\)
\(=x\left(x^2-4x+4-y^2\right)\)
\(=x\left[\left(x^2-4x+4\right)-y^2\right]\)
\(=x\left[\left(x-2\right)^2-y^2\right]\)
\(=x\left(x-2-y\right)\left(x-2+y\right)\)
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Thực hiện phép tính :
a) (4x2-5x2-3-3x2+9x) : (x2-3)
b) (4x2+4xy+y2) : (2x+y)
c) (x2-6xy+9y2) : (3y-x)
b) \(\left(4x^2+4xy+y^2\right):\left(2x+y\right)=\dfrac{\left(2x+y\right)^2}{2x+y}=2x+y\)
c) \(\left(x^2-6xy+9y^2\right):\left(3y-x\right)=\dfrac{\left(3y-x\right)^2}{3y-x}=3y-x\)
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Bài 1:Thực hiện các phép tính
a. (x5 +4x3 - 6x2):4x2
b. (x3 +x2-12) : (x-2)
c. (-2x5+3x2-4x3):2x2
d. (x3 - 64):(x2 + 4x + 16)
Bài 2:Rút gọn biểu thức
a. 3x (x - 2)- 5x (1 - x) - 8(x2 - 3)
b.(x - y) (x2 + xy + y2)+2y3
c. (x - y)2 + (x+y)2 - 2(x-y) (x+y)
Đọc tiếp
Bài 1:Thực hiện các phép tính
a. (x5 +4x3 - 6x2):4x2
b. (x3 +x2-12) : (x-2)
c. (-2x5+3x2-4x3):2x2
d. (x3 - 64):(x2 + 4x + 16)
Bài 2:Rút gọn biểu thức
a. 3x (x - 2)- 5x (1 - x) - 8(x2 - 3)
b.(x - y) (x2 + xy + y2)+2y3
c. (x - y)2 + (x+y)2 - 2(x-y) (x+y)
a) \(\left(x^5+4x^3-6x^2\right):4x^2\)
\(=\left(x^5:4x^2\right)+\left(4x^3:4x^2\right)+\left(-6x^2:4x^2\right)\)
\(=\dfrac{1}{4}x^3+x-\dfrac{3}{2}\)
b)
Vậy \(\left(x^3+x^2-12\right):\left(x-2\right)=x^2+3x+6\)
c) (-2x5 : 2x2) + (3x2 : 2x2) + (-4x^3 : 2x^2)
= \(-x^3+\dfrac{3}{2}-2x\)
d) \(\left(x^3-64\right):\left(x^2+4x+16\right)\)
\(=\left(x-4\right)\left(x^2+4x+16\right):\left(x^2+4x+16\right)\)
\(=x-4\)
(dùng hẳng đẳng thức thứ 7)
Bài 2 :
a) 3x(x - 2) - 5x(1 - x) - 8(x2 - 3)
= 3x2 - 6x - 5x + 5x2 - 8x2 + 24
= (3x2 + 5x2 - 8x2) + (-6x - 5x) + 24
= -11x + 24
b) (x - y)(x2 + xy + y2) + 2y3
= x3 - y3 + 2y3
= x3 + y3
c) (x - y)2 + (x + y)2 - 2(x - y)(x + y)
= (x - y)2 - 2(x - y)(x + y) + (x + y)2
= [(x - y) + x + y)2 = [x - y + x + y] = (2x)2 = 4x2
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Bài 1 :
a]= \(\frac{1}{4}\)x3 + x - \(\frac{3}{2}\).
b] => [x3 + x2 -12 ] = [ x2 +3 ][x-2] + [-6]
c]= -x3 -2x +\(\frac{3}{2}\).
d] = [ x3 - 64 ] = [ x2 + 4x + 16][ x- 4].
Phân tích các đa thức sau thành nhân tử: a) x2 - 9 - x2 (x2 - 9) d) x2 + 5x + 6 h) a2 + b2 + 2a – 2b – 2ab b) x2(x-y) + y2(y-x) e) 3x2 – 4x – 4 i) (x + 1)2 – 2(x + 1)(y – 3) + (y – 3)2c) x3+27+(x+3)(x-9) g) x4 + 64y4 k) x2(x + 1) – 2x(x + 1) + x + 1Mình đang cần gấp ạ
Đọc tiếp
Phân tích các đa thức sau thành nhân tử:
a) x2 - 9 - x2 (x2 - 9) d) x2 + 5x + 6 h) a2 + b2 + 2a – 2b – 2ab
b) x2(x-y) + y2(y-x) e) 3x2 – 4x – 4 i) (x + 1)2 – 2(x + 1)(y – 3) + (y – 3)2
c) x3+27+(x+3)(x-9) g) x4 + 64y4 k) x2(x + 1) – 2x(x + 1) + x + 1
Mình đang cần gấp ạ
a: \(x^2-9-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(1-x^2\right)\)
\(=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\)
b: \(x^2\left(x-y\right)+y^2\left(y-x\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)=\left(x-y\right)^2\cdot\left(x+y\right)\)
c: \(x^3+27+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)
\(=\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)
d: \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
e: \(3x^2-4x-4\)
\(=3x^2-6x+2x-4\)
\(=3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x+2\right)\)
g: \(x^4+64y^4\)
\(=x^4+16x^2y^2+64y^4-16x^2y^2\)
\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2+8y^2-4xy\right)\left(x^2+8y^2+4xy\right)\)
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h: \(a^2+b^2+2a-2b-2ab\)
\(=a^2-2ab+b^2+2a-2b\)
\(=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)
i: \(\left(x+1\right)^2-2\left(x+1\right)\left(y-3\right)+\left(y-3\right)^2\)
\(=\left(x+1-y+3\right)^2\)
\(=\left(x-y+4\right)^2\)
k: \(x^2\left(x+1\right)-2x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
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