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a) x2 - 7x + 5 = ( x2 - 2 . 7/2 . x + 49 / 4 ) + 5 - 49 / 4
= (x - 7/2)^2 - 29/4
= (x - 7/2)^2 - (√ 29 / 2 )^2
= ( x - ( 7 + √ 29 / 2 )). ( x + ( 7 - √ 29 / 2 ))
a) x4 - x5 = x4( x - 1 )
b) -8x2y2 - 12xy3 - 4xy2
= -4xy( 2xy + 3y2 + y )
c) ( x - y )3 - x3 + y3
= x3 - 3x2y + 3xy2 - y3 - x3 + y3
= 3xy2 - 3x2y
= 3xy( y - x )
a) \(\left(x^2-2x+1\right)-\left(y^2+2y+1\right)\)
\(=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-y-2\right)\left(x+y\right)\)
a) Xem lại đề
b) x³ - 4x²y + 4xy² - 9x
= x(x² - 4xy + 4y² - 9)
= x[(x² - 4xy + 4y² - 3²]
= x[(x - 2y)² - 3²]
= x(x - 2y - 3)(x - 2y + 3)
c) x³ - y³ + x - y
= (x³ - y³) + (x - y)
= (x - y)(x² + xy + y²) + (x - y)
= (x - y)(x² + xy + y² + 1)
d) 4x² - 4xy + 2x - y + y²
= (4x² - 4xy + y²) + (2x - y)
= (2x - y)² + (2x - y)
= (2x - y)(2x - y + 1)
e) 9x² - 3x + 2y - 4y²
= (9x² - 4y²) - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x - 2y)
= (3x - 2y)(3x + 2y - 1)
f) 3x² - 6xy + 3y² - 5x + 5y
= (3x² - 6xy + 3y²) - (5x - 5y)
= 3(x² - 2xy + y²) - 5(x - y)
= 3(x - y)² - 5(x - y)
= (x - y)[(3(x - y) - 5]
= (x - y)(3x - 3y - 5)
a, \(x^3-x^2y-xy^2+y^3\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x^2-y^2\right)\left(x-y\right)\)
\(=\left(x-y\right)^2\left(x+y\right)\)
b, \(x^3+x^2-4x-4\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x^2-4\right)\left(x+1\right)=\left(x-2\right)\left(x+2\right)\left(x+1\right)\)
c, \(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)=\left(x^2-1\right)\left(x-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
d, \(\left(7x+3\right)^2-\left(2x-1\right)^2\)
\(=\left(7x+3-2x+1\right)\left(7x+3+2x-1\right)\)
\(=\left(5x+4\right)\left(9x+2\right)\)
e, \(x^3-3x^2-3x+1\) sai đề
f, \(x^2-2x-3\)
\(=x^2-3x+x-3=x\left(x-3\right)+\left(x-3\right)\)
\(=\left(x+1\right)\left(x-3\right)\)
g, \(x^2-2x-8\)
\(=x^2-4x+2x-8=x\left(x-4\right)+2\left(x-8\right)\)
\(=\left(x+2\right)\left(x-8\right)\)
h, \(x^2-10x+21\)
\(=x^2-7x-3x+21\)
\(=x\left(x-7\right)-3\left(x-7\right)=\left(x-3\right)\left(x-7\right)\)
i, \(x^2-4xy+3y^2\)
\(=x^2-4xy+4y^2-y^2\)
\(=\left(x-2y\right)^2-y^2\)
\(=\left(x-2y-y\right)\left(x-2y+y\right)\)
\(=\left(x-3y\right)\left(x-y\right)\)
a) \(x^3 - x^2y - xy^2 + y^3\)
\(=\left(x^3-x^2y\right)-\left(xy^2-y^3\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)^2\left(x+y\right)\)
b) \(x^3 + x^2 - 4x - 4\)
\(=\left(x^3+x^2\right)-\left(4x+4\right)\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4\right)\)
\(=\left(x+1\right)\left(x^2-2^2\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-2\right)\)
Bài 1:
b: =x^2-10x+x-10
=(x-10)(x+1)
c: \(=2x^2-5x+2x-5=\left(2x-5\right)\left(x+1\right)\)
d: \(=3x^2+5x-3x-5=\left(3x+5\right)\left(x-1\right)\)
e: \(=\left(2x+y\right)^3\)
Bài 1:
a) 2x^2 -3x + 1 = 2x^2 -2x -x +1 = 2x.(x-1) - (x-1) = (x-1).(2x-1)
b) 2x^3y - 2xy^3 - 4xy^2 - 2xy = 2xy.(x^2 - y^2 - 2y -1) = 2xy.[ x^2 - (y^2 + 2y+1)] = 2xy.[x^2 - (y+1)^2]
= 2xy.(x-y-1).(x+y+1)
c) (x^2 + x+3).(x^2 + x +5) - 8 = (x^2+x+4-1).(x^2+x+4+1) - 8 = (x^2+x+4)^2 - 1 - 8 = (x^2+x+4)^2 - 3^2
= (x^2+x+4-3).(x^2+x+4+3) = (x^2+x+1).(x^2+x+7)
Bài 2:
a) (x+2).(x^2-2x+4) - (x^3+2x) = 0
x^3 + 8 - x^3 - 2x = 0
8 - 2x = 0
x = 4
b) x^2 - 2x - 8 = 0
x^2 +2x - 4x - 8 = 0
x.(x+2) - 4.(x+2) = 0
(x+2).(x-4) = 0
...
bn tự làm tiếp nha
a, \(\left(2x+1\right)^2-2\left(2x+1\right)\left(x-3\right)+\left(x-3\right)^2\)
\(=\left(2x+1-x+3\right)^2=\left(x+4\right)^2\)
b, \(xy+xz+3y+3z=x\left(y+z\right)+3\left(y+z\right)=\left(x+3\right)\left(y+z\right)\)
c, \(xy-xz+y-z=x\left(y-z\right)+\left(y-z\right)=\left(x+1\right)\left(y-z\right)\)
d, \(x^2-xy-8x+8y=\left(x^2-xy\right)-\left(8x-8y\right)\)
\(=x\left(x-y\right)-8\left(x-y\right)=\left(x-8\right)\left(x-y\right)\)
e, \(x^2+2xy+y^2-xz-yz=\left(x^2+2xy+y^2\right)-\left(xz+yz\right)\)
\(=\left(x+y\right)^2-z\left(x+y\right)=\left(x+y+z\right)\left(x+y\right)\)
f, \(25-4x^2-4xy-y^2=25-\left(4x^2+4xy+y^2\right)\)
\(=5^2-\left(2x+y\right)^2=\left(5-2x-y\right)\left(5+2x+y\right)\)
1,
a, (2x + 1- x + 3)2 = (x+4)2
b,\(x\left(y+z\right)+3\left(y+z\right)=\left(y+z\right)\left(x+3\right)\)
c, \(x\left(y-z\right)+\left(y-z\right)=\left(y-z\right)\left(x+1\right)\)
d,\(x\left(x-y\right)+8\left(y-x\right)\)=\(\left(x-y\right)\left(x-8\right)\)
e,\(\left(x+y\right)^2-z\left(x+y\right)\)=\(\left(x+y\right)\left(x+y-z\right)\)
f,\(25-\left(4x^2+4xy+y^2\right)=5^2-\left(2x+y\right)^2\)
\(=\left(5+2x+y\right)\left(5-2x-y\right)\)
Chúc các bn hc tốt
a)\(8x^2+4xy=4x\left(2x+y\right)\)
Xin lỗi mình chỉ biết làm câu a
Chào bạn, sau đây là câu tl của mk:
a) 8x2 + 4xy = 4x.(2x + y)
b) x3 + 27 - 3x.(x + 3) = (x + 3)(x2 - 3x + 9) - 3x.(x + 3)
= (x + 3)(x2 - 3x + 9 - 3x)
= (x + 3)(x2 - 6x + 9)
= (x + 3)(x2 - 3x - 3x + 9)
= (x + 3)[x(x - 3) - 3(x - 3)]
= (x + 3)(x - 3)2
c) x3 + 2x2 + xy2 - 9x = x(x2 + 2x + y2 - 9)
d) 2x2 - 50 +2y2 + 4xy = (2x2+ 4xy + 2y2) - 50
= 2(x2 + 2xy + y2) - 2.25
= 2.(x + y)2 - 2.52 = 2.[(x + y)2 - 52]
= x.(x + y + 5)(x + y - 5)
Chúc bạn học tốt!