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a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
b1:
câu a,f áp dụng a2-b2=(a-b)(a+b)
câu b,c áp dụng a3-b3=(a-b)(a2+ab+b2)
câu d: \(x^2+2xy+x+2y=x\left(x+2y\right)+\left(x+2y\right)=\left(x+1\right)\left(x+2y\right)\)
câu e: \(7x^2-7xy-5x+5y=7x\left(x-y\right)-5\left(x-y\right)=\left(7x-5\right)\left(x-y\right)\)
câu g xem lại đề
a) \(2x^2y^2-\frac{4}{3}x^2y+2xy\)
\(=xy\left(2xy-\frac{4}{3}x+2\right)\)
b) 2xy2.(x + 5y) - 4xy(5y + x)
= (5y + x)(2xy2 - 4xy)
= 2xy(5y + x)(y - 2)
c) 25 - 4x2 - y2 + 4xy
= 25 - (4x2 - 4xy + y2)
= 52 - (2x + y)2
= (5 - 2x - y)(5 + 2x + y)
d) x2 + 4x - 2xy - 4y +y2
= (x2 - 2xy + y2) + (4x - 4y)
= (x - y)2 + 4(x - y)
= (x - y)(x - y + 4)
e) 12y3 - 3x2y + 12xy - 12y
= 3y(4y2 - x2 + 4x - 4)
= 3y[4y2 - (x - 2)2]
= 3y(2y - x + 2)(2y + x - 2)
f) 64x4 + y4
= (8x2)2 + 16x2y2 + y4 - 16x2y2
= (8x2 + y2)2 - (4xy)2
= (8x2 + y2 - 4xy)(8x2 + y2 + 4xy)
a) \(2x^2y^2-\frac{4}{3}x^2y+2xy\)
b) \(2xy^2\left(x+5y\right)-4xy\left(5y+x\right)\)
\(=\left(x+5y\right)\left(2xy^2-4xy\right)\)
\(=2\left(x+5y\right)\left(xy^2-2xy\right)\)
c) \(25-4x^2-y^2+4xy\)
\(=25-\left(4x^2+y^2-4xy\right)\)
\(=5^2-\left[\left(2x\right)^2-2.2x.y+y^2\right]\)
\(=5^2-\left(2x-y\right)^2\)
\(=\left(5-2x+y\right)\left(5+2x-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y\right)+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(12y^3-3x^2y+12xy-12y\)
f) \(64x^4+y^4\)
\(=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2+4xy\right)\left(8x^2+y^2-4xy\right)\)
a) x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y )( x + 2 + y )
b) x2 - 2xy + y2 - 1
= ( x2 - 2xy + y2 ) - 1
= ( x - y )2 - 12
= ( x - y - 1 )( x - y + 1 )
c) x2 - 2xy + y2 - 4
= ( x2 - 2xy + y2 ) - 4
= ( x - y )2 - 22
= ( x - y - 2 )( x - y + 2 )
d) x2 - 2xy + y2 - z2
= ( x2 - 2xy + y2 ) - z2
= ( x - y )2 - z2
= ( x - y - z )( x - y + z )
e) 25 - x2 + 4xy - 4y2
= 25 - ( x2 - 4xy + 4y2 )
= 52 - ( x - 2y )2
= ( 5 - x + 2y )( 5 + x - 2y )
f) x2 + y2 - 2xy - 4z2
= ( x2 - 2xy + y2 ) - 4z2
= ( x - y )2 - ( 2z )2
= ( x - y - 2z )( x - y + 2z )
phân tích đa thức sau thành nhân tử:
a) x5 + x + 1
b) x2 - 4xy + 4y2 - 2x + 4y - 35
c) x4 - 5x2y2 + 4y2
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
a) 2xy2 - 6x2y + 4xy
= 2xy.(y - 3x + 2)
b) x2 - y2 - 5x + 5y
= (x+y).(x-y) - 5.(x-y)
= (x-y).(x+y-5)
c) x2 - 4y2 - 1 + 4y
= x2 - (4y2 - 4y + 1)
= x2 - [ (2y)2 - 2.2.y.1 + 12 ]
= x2 - (2y-1)2
= (x+2y-1).(x-2y+1)