Phân tích các đa thức sau thành nhân tử
a)3x+3y−x2−2xy−y23x+3y-x^2-2xy-y^23x+3y−x2−2xy−y2
b)15x2−15xy−25x+25y15x^2-15xy-25x+25y15x2−15xy−25x+25y
Lời giải:
a) 3x+3y−x2−2xy−y23x+3y-x^2-2xy-y^23x+3y−x2−2xy−y2
=3(x+y)−(x2+2xy+y2)=3(x+y)-(x^2+2xy+y^2)=3(x+y)−(x2+2xy+y2)
=3(x+y)−(x+y)2=(x+y)(3−x−y)=3(x+y)-(x+y)^2=(x+y)(3-x-y)=3(x+y)−(x+y)2=(x+y)(3−x−y)
b) 15x2−15xy−25x+25y15x^2-15xy-25x+25y15x2−15xy−25x+25y
=(15x2−15xy)−(25x−25y)=(15x^2-15xy)-(25x-25y)=(15x2−15xy)−(25x−25y)
=15x(x−y)−25(x−y)=(x−y)(15x−25)=15x(x-y)-25(x-y)=(x-y)(15x-25)=15x(x−y)−25(x−y)=(x−y)(15x−25)
=5(x−y)(3x−5)=5(x-y)(3x-5)=5(x−y)(3x−5)
a) x5+x3−x2−1x^5+x^3-x^2-1x5+x3−x2−1
b)x4−3x3−x+3x^4-3x^3-x+3x4−3x3−x+3
c)x3−x2y−xy2+y3x^3-x^2y-xy^2+y^3x3−x2y−xy2+y3
a)
x5+x3−x2−1=(x5−x2)+(x3−1)x^5+x^3-x^2-1=(x^5-x^2)+(x^3-1)x5+x3−x2−1=(x5−x2)+(x3−1)
=x2(x3−1)+(x3−1)=(x2+1)(x3−1)=x^2(x^3-1)+(x^3-1)=(x^2+1)(x^3-1)=x2(x3−1)+(x3−1)=(x2+1)(x3−1)
=(x2+1)(x−1)(x2+x+1)=(x^2+1)(x-1)(x^2+x+1)=(x2+1)(x−1)(x2+x+1)
b) x4−3x3−x+3=(x4−x)−(3x3−3)x^4-3x^3-x+3=(x^4-x)-(3x^3-3)x4−3x3−x+3=(x4−x)−(3x3−3)
=x(x3−1)−3(x3−1)=x(x^3-1)-3(x^3-1)=x(x3−1)−3(x3−1)
=(x3−1)(x−3)=(x−1)(x2+x+1)(x−3)=(x^3-1)(x-3)=(x-1)(x^2+x+1)(x-3)=(x3−1)(x−3)=(x−1)(x2+x+1)(x−3)
c) x3−x2y−xy2+y3x^3-x^2y-xy^2+y^3x3−x2y−xy2+y3
=x2(x−y)−y2(x−y)=x^2(x-y)-y^2(x-y)=x2(x−y)−y2(x−y)
=(x−y)(x2−y2)=(x−y)(x−y)(x+y)=(x−y)2(x+y)=(x-y)(x^2-y^2)=(x-y)(x-y)(x+y)=(x-y)^2(x+y)=(x−y)(x2−y2)=(x−y)(x−y)(x+y)=(x−y)2(x+y)
Cho 2x2 + y2 + z2 - 2x - 2xy + 2z + 2= 0. Tính giá trị biểu thức P = x+y+z
Phân tích đa thức thành nhân tử ( phối hợp các phương pháp )
1) y2 + ( 3b + 2a )xy + 6abx2
2) ab( x - y )3 + 8ab
3) x2 - ( 2a + b )xy + 2aby2
4) xy( a2 + 2b2 ) + ab( 2x2 + y2 )
5) 3xy( a2 + b2 ) - ab( x2 + 9y2 )
6) ( xy + 4ab )2 + 4( ay - bx )2
Các bạn giải cho mình 6 câu này nha . Mình đag cần gấp .
tìm GTLN: -x^2+2xy-4y^2+2x+10y-8
Phân tích đa thức thành nhân tử
a,x(y2+z2)+y(z2+x2)+z(x2+y2)+2abca,x\left(y^2+z^2\right)+y\left(z^2+x^2\right)+z\left(x^2+y^2\right)+2abca,x(y2+z2)+y(z2+x2)+z(x2+y2)+2abc
1) x2 ( a - b ) m - 2xy( a - b ) + ay2 - by2
2) 10a3 - 10a
3) 16a3 xy - 54b3 xy4
4) 16 + 2x3 y3
5) ( a + b )3 + c3
Các bạn giải cho mình nhé . Mình đag cần gấp.
a) (x+1)4+(x2+x+1)2\left(x+1\right)^4+\left(x^2+x+1\right)^2(x+1)4+(x2+x+1)2
b) (a+b−2c)3+(b+c−2a)3+(c+a−2b)3\left(a+b-2c\right)^3+\left(b+c-2a\right)^3+\left(c+a-2b\right)^3(a+b−2c)3+(b+c−2a)3+(c+a−2b)3
c) (x2−x+2)2+(x−2)2\left(x^2-x+2\right)^2+\left(x-2\right)^2(x2−x+2)2+(x−2)2
d) (x2−8)2+36\left(x^2-8\right)^2+36(x2−8)2+36
4x2-17xy+13y2
1) xy( a2 + 2b2 ) - ab( 2x2 + y2 )
2) ( xy - ab )2 + ( bx - ay )2
3) ( 2xy + ab )2 + ( 2ay - bx )2
Các bạn giải gấp cho mình nha . Mình đag cần rất gấp .
1) x2 - ( a + b )xy + aby2
2) x2 + ( 2a + b )xy + 2aby2
3) xy( a2 + b2 ) - ab( x2 + y2 )
4) xy( a2 + 2b2 ) - ab( 2x2 + y2 )
5) ( xy - ab )2 + ( bx - ay )2
6) ( 2xy + ab )2 + ( 2ay - bx )2
phân tích các đa thức sau:x^2+4x+3
4x^2+4x-3
x^2-x-12
4x^4+4x^2y^2-8y^4