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1: =(4x-1)^2-3(4x-1)
=(4x-1)(4x-1-3)
=4(x-1)(4x-1)
2: =-8x^4y^5(2y+3x)
3: =(a-5)^2-4b^2
=(a-5-2b)(a-5+2b)
5: =x^2-mx-nx+mn
=x(x-m)-n(x-m)
=(x-m)(x-n)
6: =(4a^2-3a-18-4a^2-3a)(4a^2-3a-18+4a^2+3a)
=(-6a-18)(8a^2-18)
=-6(2a-3)(2x+3)(a+3)
a) ax + ay - bx - by = ( ax - bx ) + ( ay - by ) = x( a - b ) + y( a - b ) = ( a - b )( x + y ) < đã sửa >
b) 2x2 - 6xy + 5x - 15y = 2x( x - 3y ) + 5( x - 3y ) = ( x - 3y )( 2x + 5 )
c) ( a + b )2 - 4a2 = ( a + b )2 - ( 2a )2 = ( a + b - 2a )( a + b + 2a ) = ( b - a )( b + 3a )
d) 5a2xy - 10a3x - 15a2x2 = 5a2x( y - 2a - 3x )
e) 3( x - 1 ) + 5x( x - 1 ) = ( x - 1 )( 3 + 5x )
f) 9a2 - 4 = ( 3a )2 - 22 = ( 3a - 2 )( 3a + 2 )
g) 2x3 + 8x4 + 8x = 2x( x + 4x2 + 4 )
h) a2 - 4 + 4b - b2 = a2 - ( b2 - 4b + 4 ) = a2 - ( b - 2 )2 = ( a - b + 2 )( a + b - 2 )
i) a2 + 2ab + b2 - 16 = ( a2 + 2ab + b2 ) - 16 = ( a + b )2 - 42 = ( a + b - 4 )( a + b + 4 )
k) x2 + 5x + 4 = x2 + x + 4x + 4 = x( x + 1 ) + 4( x + 1 ) = ( x + 1 )( x + 4 )
l) 2x2 - 3x - 5 = 2x2 + 2x - 5x - 5 = 2x( x + 1 ) - 5( x + 1 ) = ( x + 1 )( 2x - 5 )
m) x3 + 6x2 + 9x = x( x2 + 6x + 9 ) = x( x + 3 )2
1, 5a2xy-10a3x-15ay = 5a( axy - 2a\(^2\)x - 3y )
2, mxy-m2x+my = m( xy - mx + y )
3, 2mx-4m2xy+6mx = 2mx( 1 - 2my + 3 ) = 2mx( 4 - 2my )
4, a2b-2ab2+ab = ab( a - 2b + 1 )
5, 5a2b-2ab2+ab = ab( 5a - 2b +1 )
6, -3x2y3-6x3y2-x2y2 = -3x\(^2\)y\(^2\) ( y + 2x + 1 )
7, 5x2y4-10x4y2+5x2y2 = 5x\(^{^2y^2}\)( y\(^2\) - 2x\(^2\) + 1 )
8, -2x3y4-4x4y3+2x3y3 = 2\(x^3y^3\) ( -y - 2x + 1 )
9, 4x3y2-8x3y+16xy2-24 = 4( x\(^3\)y\(^2\) - 2x\(^3\)y + 4 xy\(^2\) - 6 )
10, 12x3y-6xy+3x = 3x( 4x\(^2\)y - 2y + 1 )
11, 2(x-y)-a(x-y) = ( 2 - a ) ( x - y )
12, a(x-y)+b(x-y)= ( a + b ) ( x - y )
13, m(x+y)-n(x+y) = ( m - n ) ( x + y )
14, 2a(x+y)-4(x+y) = ( 2a - 4 )( x + y ) = 2( a - 2 ) ( x + y )
15, 3a(x+y)-6ab(x+y) = ( 3a - 6ab )( x + y ) = 3a( 1 - 2b ) ( x + y )
16, 5a2(x-y)+10a(x-y) = ( 5a\(^2\)+10a )( x - y ) = 5a( a + 2 ) ( x - y )
17, -2ab(x-y)-4a(x-y) = ( -2ab - 4a )( x - y ) = -2a( b + 2 )( x - y )
18, 3a(x-y)+2(x-y) = ( 3a + 2 ) ( x - y )
19, m(a-b)-m2(a-b) = ( m - m\(^2\) ) ( a - b ) = m( 1 - m ) ( a - b )
20, mx(a+b)-m(a+b) = ( mx - m ) ( a + b ) = m( x - 1 )( a + b )
21, x(a-b)-y(b-a) = x( a - b ) + y( a - b ) = ( x + y ) ( a - b )
22, ab(x-5)-a2(5-x) = ab( x - 5 ) + a\(^2\)( x - 5 ) = ( ab + a\(^2\) ) ( x - 5 ) = a( b + a )( x - 5 )
23, 2a2(x-y)-4a(y-x)= 2a\(^2\)( x - y ) + 4a( x - y )=( 2a\(^2\) + 4a ) ( x - y )= 2a( a + 2 )( x - y )
Đăng ít thôi =))
a. \(5a^2xy-10a^3x-15ay=5a\left(axy-2a^2x-3y\right)\)
b. \(mxy-m^2x+my=m\left(xy-mx+y\right)\)
c. \(2mx-4m^2xy+6mx=2mx\left(1-2my+3\right)=2mx\left(-2my+4\right)\)
d. \(a^2b-2ab^2+ab=ab\left(a-2b+1\right)\)
e. \(5a^2b-2ab^2+ab=ab\left(5a-2b+1\right)\)
g.
Phá tung cái ngoặc ra thôi mà nhỉ?
a) \(\left(3x-5\right)\left(3x+b\right)=9x^2+\left(3b-15\right)x-5b\)
Đồng nhất hệ số ta có: \(\left\{{}\begin{matrix}9=a\\3b-15=1\\-5b=c\end{matrix}\right.\) giải cái hệ 3 pt này là thu được a, b, c
\(\dfrac{3a^2x^2\left[ax\left(4a-5x\right)+7ax\right]+a^2x^3\left[15\left(a+x\right)-21\right]}{9a^3x^3}\)
\(=\dfrac{3a^2x^2\left(4a^2x-5ax^2+7ax\right)+a^2x^3\left(15a+15x-21\right)}{9a^3x^3}\)
\(=\dfrac{a^2x^2\left[3\left(4a^2x-5ax^2+7ax\right)+15a+15x-21\right]}{9a^3x^3}\)
\(=\dfrac{3\left(4a^2x-5ax^2+7ax\right)+3\left(5a+5a-7\right)}{9ax}\)
\(=\dfrac{4a^2x-5ax^2+7ax+5a+5x-7}{3ax}\)
Chúc bạn học tốt!!!