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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 )
\(\left(x^2-5x+8\right)^2-6x+8\)
\(=x^4+25x^2+64-10x^3-80x+16x^2-6x+8\)
\(=x^4-10x^3+41x^2-86x+72\)
\(=x^3\left(x-2\right)-8x^2\left(x-2\right)+25x\left(x-2\right)-36\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-8x^2+25x-36\right)\)
\(=\left(x-2\right)\left[x^2\left(x-4\right)-4x\left(x-4\right)+9\left(x-4\right)\right]\)
\(=\left(x-2\right)\left(x-4\right)\left(x^2-4x+9\right)\)
ta có: \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2=\left(a+b+c\right)^2+\left(a+b-c-2c\right)\left(a+b-c+2c\right).\)
\(=\left(a+b+c\right)^2+\left(a+b-3c\right)\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)
(a+b+c)^2+(a+b-c)^2-4c^2
=(a^2+b^2+c^2+2ab+2bc+2ac)+(a^2-2ab+b^2-2ac+c^2-abc)-4c^2
=a^2+b^2+c^2+2ab+2bc+2ac+a^2-2ab+b^2-2ac+c^2-abc-4c^2
=(a^2+a^2)+(b^2+b^2)+(c^2+c^2)+(2ab-2ab)+(2bc-2bc)+(2ac-2ac)-4c^2
=2a^2+2b^2+2c^2-4c^2
=(2a^2+2b^2)+(2c^2-4c^2)
=2*(a^2+b^2)+2c^2*(1-2)
a) = (xyz+xy) +(z+1) +(yz+zx)+(x+y)
= xy(z+1) +(z+1)+z(x+y)+(x+y)
= (z+1)(xy+1)+(x+y)(Z+1)
=(z+1)(xy+1+x+y)
\(a\left(b^2+c^2\right)+b\left(a^2+c^2\right)+c\left(b^2+a^2\right)+2abc\)
\(=ab^2+ac^2+a^2b+bc^2+cb^2+a^2c+2abc\)
\(=\left(a^2b+a^2c+ab^2+abc\right)+\left(abc+ac^2+b^2c+bc^2\right)\)
\(=a\left(ab+ac+b^2+bc\right)+c\left(ab+ac+b^2+bc\right)\)
\(=\left(a+c\right)\left(ab+ac+b^2+bc\right)\)
\(=\left(a+c\right)\left[\left(ab+ac\right)+\left(b^2+bc\right)\right]\)
\(=\left(a+c\right)\left[a\left(b+c\right)+b\left(b+c\right)\right]\)
\(=\left(a+c\right)\left(b+c\right)\left(a+b\right)\)