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mình chỉ phân tích thôi
a) 6x(4-x)+x-4
=6x(4-x)-(4-x)
=(6x-1)(4-x)
c) 25x^2-10x+1-16z^2
=(5x-1)^2-16z^2
=(5x-1-4z)(5x-1+4z)
ban xem lại đề bài câu b đi chắc là sai đó
còn các câu trên bạn tự làm nhé
Thực hiện phép tính:
a) (2x-3y)(4x2+6xy+9y2)
=8x3-27y3
b) (6x3+3x2+4x+2):(3x2+2)
=(3x2+2)(2x+1):(3x2+2)
=2x+1
c) (x+2)2+(3-x)-2(x+3)(x-3)
=x2+4x+4+3-x-2x2+18
=-x2+4x+25
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
1) -25x6 - y8 + 10x3y4 = -( 25x6 - 10x3y4 + y8 ) = -[ ( 5x3 )2 - 2.5x3.y4 + ( y4 ) ] = -( 5x3 - y4 )2
2) 2x( 3x - 5 ) + 10 - 6x = 2x( 3x - 5 ) - 2( 3x - 5 ) = ( 3x - 5 )( 2x - 2 ) = 2( 3x - 5 )( x - 1 )
3) x2 - 9 - x2( x2 - 9 ) = ( x2 - 9 ) - x2( x2 - 9 ) = ( x2 - 9 )( 1 - x2 ) = ( x - 3 )( x + 3 )( 1 - x )( 1 + x )
4) 4x2 - 9 - ( 3x + 1 )( 2x - 3 ) = ( 2x - 3 )( 2x + 3 ) - ( 3x + 1 )( 2x - 3 )
= ( 2x - 3 )[ ( 2x + 3 ) - ( 3x + 1 ) ]
= ( 2x - 3 )( 2x + 3 - 3x - 1 )
= ( 2x - 3 )( 2 - x )
5) 8x3 - y3 - 4x + 2y = ( 8x3 - y3 ) - ( 4x - 2y )
= [ ( 2x )3 - y3 ) - 2( 2x - y )
= ( 2x - y )( 4x2 + 2xy + y2 ) - 2( 2x - y )
= ( 2x - y )( 4x2 + 2xy + y2 - 2 )
\(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
a) \(x^2-81=\left(x-9\right)\left(x+9\right)\)
b) \(4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
c) \(x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
d) \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
e) \(6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)
f) \(x^2-4x^2+4y^2+4xy=\left(x^2+4xy+4y^2\right)-4x^2=\left(x+2y\right)^2-4x^2\\ =\left(x+2y+2x\right)\left(x+2y-2x\right)=\left(3x+2y\right)\left(2y-x\right)\)
g) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2a\left(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right)=2a\left(a^2+3b^2\right)\)
h) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)
Bài 2:
a: 6x(4-x)+(x-4)
=6x(4-x)-(4-x)
=(4-x)(6x-1)
b: \(=x^2-1+y\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(1+y\right)=\left(y+1\right)\left(x+1\right)\left(x-1\right)\)
c: \(=\left(5x-1\right)^2-\left(4z\right)^2\)
=(5x-1-4z)(5x-1+4z)