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1.a) 2x4-4x3+2x2
=2x2(x2-2x+1)
=2x2(x-1)2
b) 2x2-2xy+5x-5y
=2x(x-y)+5(x-y)
=(2x+5)(x-y)
2.
a) 4x(x-3)-x+3=0
=>4x(x-3)-(x-3)=0
=>(4x-1)(x-3)=0
=> 2 TH:
*4x-1=0 *x-3=0
=>4x=0+1 =>x=0+3
=>4x=1 =>x=3
=>x=1/4
vậy x=1/4 hoặc x=3
b) (2x-3)^2-(x+1)^2=0
=> (2x-3-x-1).(2x-3+x+1)=0
=>(x-4).(3x-2)=0
=> 2 TH
*x-4=0
=> x=0+4
=> x=4
*3x-2=0
=>3x=0-2
=>3x=-2
=>x=-2/3
vậy x=4 hoặc x=-2/3
\(1,3x-24y=3\left(x-8y\right)\)
\(2,6x^3y^2-12x^2y^2-3x^2y=3x^2y\left(2xy-4y-1\right)\)
\(3,7x\left(x-2\right)-8\left(x-2\right)=\left(x-2\right)\left(7x-8\right)\)
...(tương tự)
\(10,5x-5y+x^2-xy=5\left(x-y\right)+x\left(x-y\right)=\left(x-y\right)\left(x+5\right)\)
\(11,x^2+2xy+y^2-16=\left(x+y\right)^2-16=\left(x+y-4\right)\left(x+y+4\right)\)
a) \(x^4+4x^2-5=x^4+4x^2+4-9=\left(x^2+2\right)^2-3^2\)
\(\left(x^2+2-3\right)\left(x^2+2+3\right)\)
b) \(-x-y^2+x^2-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)\(=\left(x+y\right)\left(x-y-1\right)\)
c) \(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
d) \(x^2-5x+5y-y^2=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
e) \(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)\)
\(=5\left(x-y\right)\left(x^2-2x\right)\)
f) \(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)
a, \(4y^2+1-4y=\left(2y\right)^2-2.2y.1+1^2=\left(2y-1\right)^2\)
b, \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(3x-5\right)\left(x-y\right)\)
c, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
Câu 1 :
\(a,\left(x-1\right)-\left(x^2-x\right)\)
\(=x-1-x^2+x\)
\(=-x^2+2x-1\)
\(=-\left(x-1\right)^2\)
\(b,\left(x+1\right)+\left(x-1\right)\)
\(=x+1+x-1\)
\(=2x\)
Câu 2 :
\(a,6x^2+3x=3x\left(2x+1\right)\)
\(b,x.\left(x+y\right)-5x-5y\)
\(=x^2+xy-5x-5y\)
\(=\left(x^2-5x\right)+\left(xy-5y\right)\)
\(=x\left(x-5\right)+y\left(x-5\right)\)
\(=\left(x-5\right)\left(x+y\right)\)
\(c,4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
\(d,6x^2-7x+1\)
\(=6x^2-6x-x+1\)
\(=6x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(6x-1\right)\)
1/a ) = (x+y)3 -(x+y)
= (x+y)[(x+y)2+1]
c) = 5(x2-xy+y2)-20z2
=5(x-y)2-20z2
= 5 [ (x-y)2- 4z2 ]
=5(x-y-4z)(x-y+4z)
Bài 1:
a) x3-x+3x2y+3xy2+y3-y
=x3+2x2y-x2+xy2-xy+x2y+2xy2-xy+y3-y2+x2+2xy-x+y2-y
=x(x2+2xy-x+y2-y)+y(x2+2xy-x+y2-y)+(x2+2xy-x+y2-y)
=(x2+2xy-x+y2-y)(x+y+1)
=[x(x+y-1)+y(x+y-1)](x+y+1)
=(x+y-1)(x+y)(x+y+1)
c) 5x2-10xy+5y2-20z2
=-5(2xy-y2+4z2-2)
Bài 2:
5x(x-1)=x-1
=>5x2-6x+1=0
=>5x2-x-5x+1
=>x(5x-1)-(5x-1)
=>(x-1)(5x-1)=0
=>x=1 hoặc x=1/5
b) 2(x+5)-x2-5x=0
=>2(x+5)-x(x+5)=0
=>(2-x)(x+5)=0
=>x=2 hoặc x=-5
\(a,\left(2x-y\right)^2=4x^2-4xy+y^2\)
\(b,\left(5x-7y^2\right).\left(5x+7y^2\right)=\left(25x^2-49y^4\right)\)
\(c,\left(5x-7y\right)^2.\left(5x+7y\right)^2=\left(25x^2-70xy+49x^2\right).\left(25x^2+70xy+49x^2\right)\)
\(d,\left(\frac{1}{3}x+5y\right).\left(5y-\frac{1}{3}x\right)=25y^2-\frac{1}{9}x^2\)
học tốt nha
a) (2x-y)2 = (2x)2 - 2.2x.y + y2 =4x2-4xy+y2
b)(5x-7y2).(5x+7y2) = (5x)2 - (7y2) 2 =25x2 - 49y4
câu c,d mk ko bít làm
a, \(\left(5x-4\right)\left(5x+4\right)-\left(5x-4\right)^2=\left(25x^2-16\right)-\left(25x^2-40x+16\right)=40x-32\)
b,\(\left(5x+3\right)^2-\left(4x-1\right)^2-\left(9x^2+8\right)=\left(x+4\right)\left(9x-2\right)-\left(9x^2+8\right)\)
\(=9x^2+34x-8-\left(9x^2+8\right)=34x\)
c,\(2\left(x-5y\right)\left(x+5y\right)+\left(x+5y\right)^2+\left(x-5y\right)^2=\left(2x\right)^2=4x^2\)