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a)x^2+2x-4y^2-4y
=(x2-4y2)+(2x-4y)
=(x-2y)(x+2y)+2.(x-2y)
=(x-2y)(x+2y+2)
b)x^4-6x^3+54x-81
=(x4-81)+(-6x3+54x)
=(x2-9)(x2+9)-6x.(x2-9)
=(x2-9)(x2+9-6x)
=(x-3)(x+3)(x-3)2
=(x-3)3(x+3)
c)ax^2+ax-bx^2-bx-a+b
=(ax2-bx2)+(ax-bx)+(-a+b)
=x2.(a-b)+x.(a-b)-(a-b)
=(a-b)(x2+x+1)
a) \(ax+ay-3x-3y=a\left(x+y\right)-3\left(x+y\right)=\left(a-3\right)\left(x+y\right)\)
b) \(x^3-3x^2+3x-9=x^2\left(x-3\right)+3\left(x-3\right)=\left(x-3\right)\left(x^2+3\right)\)
c) xem lại đề
d) \(9-x^2-2xy-y^2=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)
ax2 - ax + bx2 -bx + a + b
= (ax2+ bx2 ) - (ax + bx) + (a + b)
=x2 (a + b) - x(a + b) + (a + b)
= (x2 - x + 1)(a + b)
ax2 - ax + bx2 - bx + a + b
= ( ax2 + bx2 ) - ( ax + bx ) + ( a + b )
= x2( a + b ) - x( a + b ) + ( a + b )
= ( a + b )( x2 - x + 1 )
Ta có
\(x^4+6x^2+25=\left(x^4+10x^2+25\right)-4x^2\)
\(=\left(x^2+5\right)^2-4x^2=\left(x^2+5-2x\right)\left(x^2+5+2x\right)\)
\(3x^4+4x^2+28x+5=\left(x^2-2x+5\right)\left(3x^2+6x+1\right)\)
\(\Rightarrow P\left(x\right)=x^2-2x+5\)
\(\Rightarrow P\left(1\right)=1-2+5=4\)
Câu 1:8-x^3=2^3-x^3=(2-x)(4+2x+x^2)
Câu 2:Ta có:x^2-5x+4
=(x^2-2x5/2+25/4)-9/4
=(x-5/2)^2-(3/2)^2
=(x-5/2-3/2)(x-5/2+3/2)
=(x-4)(x-1)
->đa thức B là:(x-4)
->hệ số tự do của đa thức B là:-4
A = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )
= 4x( ac + bc + a + b )
= 4x[ c( a + b ) + ( a + b ) ]
= 4x( a + b )( c + 1 )
B = ax - bx + cx - 3a + 3b - 3c
= x( a - b + c ) - 3( a - b + c )
= ( a - b + c )( x - 3 )
C = 2ax - bx + 3cx - 2a + b - 3c
= x( 2a - b + 3c ) - ( 2a - b + 3c )
= ( 2a - b + 3c )( x - 1 )
D = ax - bx - 2cx - 2a + 2b + 4c
= x( a - b - 2c ) - 2( a - b - 2c )
= ( a - b - 2c )( x - 2 )
E = 3ax2 + 3bx2 + ax + bx + 5a + 5b
= 3x2( a + b ) + x( a + b ) + 5( a + b )
= ( a + b )( 3x2 + x + 5 )
F = ax2 - bx2 - 2ax + 2bx - 3a + 3b
= x2( a - b ) - 2x( a - b ) - 3( a - b )
= ( a - b )( x2 - 2x - 3 )
= ( a - b )( x2 + x - 3x - 3 )
= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]
= ( a - b )( x + 1 )( x - 3 )
a) \(ax-bx+ab-x^2=\left(ax+ab\right)-\left(bx+x^2\right)=a\left(x+b\right)-x\left(x+b\right)=\left(x+b\right)\left(a-x\right).\)
b) \(x^2-2xy+y^2-9=\left(x^2-2xy+y^2\right)-3^2=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x+y+3\right).\)
Học tốt nhé ^3^
\(a.=a\left(x+b\right)-x\left(b+x\right)\)
\(=a\left(x+b\right)-x\left(x+b\right)\)
\(=\left(a-x\right)\left(x+b\right)\)
\(b.=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
_Moon_
\(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
=>a=2; b=6
a+b=2+6=8