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1/ 2a + 2b = 2( a + b )
2/ 3a - 6b - 9c = 3( a - 2b - 3c )
3/ 5ax - 15ay + 20a = 5a( x - 3y + 4 )
4/ 3a2x - 6a2y + 12a = 3a( ax - 2ay + 4 )
5/ 4a( x - 5 ) - 2( 5 - x ) = 4a( x - 5 ) + 2( x - 5 ) = ( x - 5 )( 4a + 2 ) = ( x - 5 )2( 2a + 1 )
6. -3a( x - 3 ) + ( 3 - x ) = 3a( 3 - x ) + 1( 3 - x ) = ( 3a + 1 )( 3 - x )
7/ xm+1 - xm = xm( x + 1 )
8/ xm+2 - x2 = x2( xm - 1 )
1)\(8x^6-\frac{1}{125}y^3=\left(2x^2\right)^3-\left(\frac{1}{5}y\right)^3\)
Bạn tự lm tiếp.AD HĐT số (7)
2)\(\left(x+4\right)^3-64=\left(x+4\right)^3-4^3\)
AD HĐT số (7).Tự lm tiếp
3)\(x^6+1=\left(x^2\right)^3+1\)
AD HĐT số (7).Tự lm tiếp
4)\(x^9+1=\left(x^3\right)^3+1\)
AD HĐT số (7).Tự lm tiếp
5,\(x^{12}-y^4=\left(x^6\right)^2-\left(y^2\right)^2\)
AD HĐT số (3).Tự lm tiếp
6)\(x^3+6x^2+12x+8=\left(x+2\right)^3\)
AD HĐT số (4)
7)\(x^3-15x^2+75x-125=\left(x-5\right)^3\)
AD HĐT số (5)
8)\(27a^3-54a^2b+36ab^2-8b^3\)
\(=\left(3a\right)^3-3.\left(3a\right)^2.2b+3.3a.\left(2b\right)^2-\left(2b\right)^3\)
\(=\left(3a-2b\right)^3\)
AD HĐT số (5)
Phân tích đa thức thành nhân tử:
a) Ta có: \(3x^2-8xy+5y^2\)
\(=3x^2-3xy-5xy+5y^2\)
\(=3x\left(x-y\right)-5y\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5y\right)\)
b) Ta có: \(8xy^3+x\left(x-y\right)^3\)
\(=x\left[8y^3-\left(x-y\right)^3\right]\)
\(=x\left[2y-\left(x-y\right)\right]\left[4y^2+2y\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=x\left(2y-x+y\right)\left(4y^2+2xy-2y^2+x^2-2xy+y^2\right)\)
\(=x\left(3y-x\right)\left(3y^2+x^2\right)\)
c) Ta có: \(2x\left(x-3\right)-x+3\)
\(=2x\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-3\right)\left(2x-1\right)\)
d) Ta có: \(x^4-4x^3+4x^2\)
\(=x^2\left(x^2-4x+4\right)\)
\(=x^2\cdot\left(x-2\right)^2\)
e) Ta có: \(4x^2+4xy-4z^2+y^2-4z-1\)
\(=\left(4x^2+4xy+y^2\right)-\left(4z^2+4z+1\right)\)
\(=\left(2x+y\right)^2-\left(2z+1\right)^2\)
\(=\left(2x+y-2z-1\right)\left(2x+y+2z+1\right)\)
f) Ta có: \(x^2-2xy+y^2-x+y-6\)
\(=\left(x-y\right)^2-\left(x-y\right)-6\)
\(=\left(x-y\right)^2-3\left(x-y\right)+2\left(x-y\right)-6\)
\(=\left(x-y\right)\left(x-y-3\right)+2\left(x-y-3\right)\)
\(=\left(x-y-3\right)\left(x-y+2\right)\)
g) Ta có: \(x^2\left(x+3\right)^2-\left(x+3\right)^2-\left(x^2-1\right)\)
\(=x^2\left(x^2+6x+9\right)-\left(x^2+6x+9\right)-x^2+1\)
\(=\left(x^2-6x+9\right)\left(x^2-1\right)-\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-6x+9-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2-6x+8\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x-4\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) \(x^2+4x+3=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1^2=\left(x+1\right)\left(x+3\right)\) (mình sửa lại)
b) \(x^2+8x-9=\left(x^2+8x+16\right)-25=\left(x+4\right)^2-5^2=\left(x-1\right)\left(x+9\right)\)
c) \(3x^2+6x-9=3\left[\left(x^2+2x+1\right)-4\right]=3\left[\left(x+1\right)^2-2^2\right]=3\left(x-1\right)\left(x+3\right)\)
d) \(2x^2+x-3=2x^2-4x+2+5x-5=2\left(x^2-2x+1\right)+5\left(x-1\right)=2\left(x-1\right)^2+5\left(x-1\right)=\left(x-1\right)\left(2x+3\right)\)
\(a,x^2+4xy-21y^2\\ =x^2+7xy-3xy-21y^2\\ =x\left(x+7y\right)-3y\left(x+7y\right)\\ =\left(x+7y\right)\left(x-3y\right)\\ b,5x^2+6xy+y^2\\ =5x^2+5xy+xy+y^2\\ =5x\left(x+y\right)+y\left(x+y\right)\\ =\left(x+y\right)\left(5x+y\right)\\ c.x^2+2xy-15y^2\\ =x^2+5xy-3xy-15y^2\\ =x\left(x+5y\right)-3y\left(x+5y\right)\\ =\left(x+5y\right)\left(x-3y\right)\)
Các câu sau đều tương tự
a , \(-q^3+12q^2x-48qx^2+64x^3\)
\(=-\left(q^3-12q^2x+48qx^2-64x^3\right)\)
\(=\)\(-\left(q-4x\right)^3\)
b , x2 + 2xy - y2 - 9
= - ( x2 - 2xy + y2 ) - 9
= - ( x - y )2 - 9
= ( - x + y - 3 ) ( x - y + 3 )
3 , 1 - m2 + 2mn - n2
= 1 - ( m2 - 2mn + n2 )
= 1 - ( m - n )2
= ( 1 - m + n ) ( 1 + m - n )
4 , x3 - 8 + 6a2 - 12a
= x3 + 6a2 - 12a + 8
= x3 + 6a2 - 12a + 4 + 4
= x3 + ( 6a2 - 12a + 4 ) + 4
= x3 + ( 3a - 2 )2 + 4
= ( x + 3a - 2 + 2 ) ( x2 + 3a + 2 + 2 )
( Mai làm tiếp mấy ý sau '-' muộn rồi ~ )
5 , x2 - 2xy + y2 - xz - yz
= ( x2 - 2xy + y2 ) - ( xz + yz )
= ( x - y )2 - z ( x + y )
= ( x - y ) 2 - z ( x - y )
= ( x - y ) ( x - y - z )
6 , x2 - 4xy + 4y 2 - z2 + 4z - 4t2
=( x2 - 4xy + 4y 2 ) - (z2 - 4z +4 ) . t2
= ( x - y )2 - ( z - 2 )2 . t2
= ( x - y - z - 2 ) ( x - y + z - 2 ) t2
7 , 25 - 4x2 - 4xy - y2
= 25 + ( - 4x2 - 4xy + y2 )
= 25 + ( 2x - y )2
= ( 5 + 2x - y ) ( 5 + 2x + y )
8 ,
x3 + y3 + z3 - 3xyz
= (x+y)3 - 3xy (x - y ) + z3 - 3xyz
= [ ( x + y)3 + z3 ] - 3xy ( x + y + z )
= ( x + y + z )3 - 3z ( x + y )( x + y + z ) - 3xy ( x - y - z )
= ( x + y + z )[( x + y + z )2 - 3z ( x + y ) - 3xy ]
= ( x + y + z )( x2 + y2 + z2 + 2xy + 2xz + 2yz - 3xz - 3yz - 3xy)
= ( x + y + z)(x2 + y2 + z2 - xy - xz - yz)