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\(a,\left(6x+1\right)\left(x+2\right)-2x\left(3x-5\right)\)
\(=6x^2+12x+x+2-6x^2+10x\)
\(=23x+2\)
a) (6x + 1)(x + 2) - 2x(3x - 5)
= 6x2 + 12x + x + 2 - 6x2 + 10x
= (6x2 - 6x2) + (12x + x + 10x) + 2
= 23x + 2
b) (2x - 1)2 - (2x - 3)(2x + 3)
= 4x2 - 4x + 1 - 4x2 + 9
= (4x2 - 4x2) - 4x + (1 + 9)
= -4x + 10
c) (2x - 3)3 - (3x + 1)(5 - 4x) - 16x2
= 8x3 - 36x2 + 54x - 15x + 12x2 - 5 + 4x - 16x2
= 8x3 - (36x2 - 12x2 + 16x2) + (54x - 15x + 4x) - 5
= 8x3 - 40x2 + 43x - 5
d) (3x + 2) - (x - 5) - x(3x - 13)
= 3x + 2 - x + 5 - 3x2 + 13x
= (3x - x + 13x) + (2 + 5) - 3x2
= 15x + 7 - 3x2
a,X^3-16x =x(x^2-16)
b,y(y-2)-3(y-2)=(y+3).(y-2)
c,x^2+4x+4-y^2=(x+2)^2-y^2=(x+y+2).(x+2-Y)
D,4^2y^3-12x^2y^4+16X^5y^3=4x^2y^2(y-3y^2+4X^3y)
\(a)\)
\(4x^2-y^2+2x+y\)
\(=\left(4x^2-y^2\right)+\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)+\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y+1\right)\)
\(b)\)
\(x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=x\left(x^2+5x+9\right)-3\left(x^2+5x-9\right)\)
\(=\left(x-3\right)\left(x^2+5-9\right)\)
\(c)\)
\(12x^3+4x^2-27x-9\)
\(=\left(12x^3+4x^2\right)-\left(27x+9\right)\)
\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(4x^2-9\right)\)
\(=\left(3x+1\right)[\left(2x\right)^2-3^2]\)
\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)
\(d)\)
\(16x^2+4x-y^2+y^2\)
\(=16x^2+4x\)
\(4x\left(4x+1\right)\)
a) 2x3 + 3x - 5
= 2x3 - 2x + 5x - 5
= (2x3 - 2x) + (5x - 5)
= 2x(x2-1) + 5(x-1)
= 2x(x+1)(x-1) + 5(x-1)
= (2x2+2x)(x-1) + 5(x-1)
= (x-1)(2x2+2x+5)
b) 16x - 5x^2 - 3 = - 5^2 + 16x - 3 = -5^2+15x +x - 3 = 5x(3-x) - (3-x) = (3-x)(5x-1);
c) x^2 +4x +3 = x^2 +x + 3x +3 = x(x+1) +3(x+1) = (x+3)(x+1);
d) x^2 -4x -5 = x^2 + x - 5x - 5 = x(x+1) -5 (x+1) = (x-5)(x+1)
e) 16x - 5x^2 - 3 => tương tự câu b
a) 3x2 - 3y2 - 12x + 12x
= 3( x2 - y2- 4x + 4x )
= 3( x - y)( x + y)
b) 4x3 + 4xy2 + 8x2y - 16x
= 4x( x2 + y2 + 2xy - 4)
= 4x[( x + y)2 - 22]
= 4x( x + y - 2)( x + y +2)
c) x4 - 5x2 + 4
= ( x2)2 - 2.2x2 + 22 - x2
= ( x2 - 2)2 - x2
= ( x2 - 2 - x)( x2 - 2 + x)
a) x3 - x2 - 5x + 125 = ( x\(^3\) + 125 ) - ( x\(^2\) + 5x ) = ( x + 5 ) ( x\(^2\) - 5x + 25 ) - x ( x + 5 )
= ( x + 5 ) ( x\(^2\) - 5x + 25 - x ) = ( x + 5 ) ( x\(^2\) - 6x + 25 )
b) x3 + 2x2 - 6x - 27 = ( x\(^3\) - 27 ) + ( 2x\(^2\) - 6x ) = ( x - 3 ) ( x\(^2\) + 3x + 9 ) + 2x ( x - 3 )
= ( x- 3 ) ( x\(^2\) + 3x + 9 + 2x ) = ( x - 3 ) ( x\(^2\) + 5x + 9 )
c) 12x3 + 4x2 - 27x - 9 = (12x3 + 4x2 ) - ( 27x + 9 ) = 4x\(^2\)( 3x + 1 ) - 9 ( 3x + 1 )
= ( 4x\(^2\) - 9 ) ( 3x -1 ) = ( 2x - 3 ) ( 2x + 3 ) ( 3x - 1 )
i) (x2 + 8x - 34)2 - (3x2 - 8x - 2)2
= (x2 + 8x - 34- 3x\(^2\) + 8x + 2) ( x\(^2\) + 8x - 34+3x2 - 8x - 2)
= ( -2x\(^2\) + 16x - 32 ) ( 4x\(^2\) - 36 )
= ( -2x\(^2\) + 16x - 32 ) ( 2x - 6 ) ( 2x + 6 )
a, x3- x2- 5x+ 125
=- (x2+ 5x)+ (x3+125)
=-x(x+5)+ (x+5)(x2- 5x+ 25)
=(x+5)(-x+x2- 5x+ 25)
=(x+ 5)(x2- 6x+ 25)
3) =2(x2+2xy+y2)
=2(x+y)2
6)= -3(x2+4x+4)
= -3(x2+2.x.2+22)
= -3(x+2)2
9) = 4x3y2(x2+4x+4)
=4x3y2(x+2)2
12)=2x(x2-2x+1)
=2x(x-1)2
15)= 5x2y2(x2-2x+1)
=5x2y2(x-1)2
a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
c: C=125x^3+150x^2+60x+8+125x^3-150x^2+60x-8-2(x^2-4)
=250x^3+120x-2x^2+8
=250x^3-2x^2+120x+8
d: D=(4x)^3-3^3-(4x)^3-3^3
=64x^3-27-64x^3-27
=-54
c) \(C=\left(5x+2\right)^3+\left(5x-2\right)^3-2\left(x-2\right)\left(x+2\right)\)
\(=\left[\left(5x\right)^3+3\cdot\left(5x\right)^2\cdot2+3\cdot5x\cdot2^2+2^3\right]+\left[\left(5x\right)^3-3\cdot\left(5x\right)^2\cdot2+3\cdot5x\cdot2^2-2^3\right]-2\left(x^2-4\right)\)
\(=125x^3+150x^2+60x+8+125x^3-150x^2+60x-8-2x^2+8\)
\(=\left(125x^3+125x^3\right)+\left(150x^2-150x^2-2x^2\right)+\left(60x+60x\right)+\left(8-8+8\right)\)
\(=250x^3-2x^2+120x+8\)
d) \(D=\left(4x-3\right)\left(16x^2+12x+9\right)-\left(4x+3\right)\left(16x^2-12x+9\right)\)
\(=\left(4x\right)^3-3^3-\left[\left(4x\right)^3+3^3\right]\)
\(=64x^3-27-\left(64x^3+27\right)\)
\(=64x^3-27-64x^3-27\)
\(=-27-27\)
\(=-54\)