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\(a.\left(2x-3\right)\left(4x^2+6x+9\right)-\left(2x+3\right)\left(4x^2-6x+9\right)\\ =\left(2x\right)^3-3^3-\left[\left(2x\right)^3+3^3\right]\\ =8x^3-9-\left(8x^3+9\right)\\ =8x^3-9-8x^3-9=-18\)
\(b.\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\\ =x^3+1-\left(x^3-1\right)\\ =x^3+1-x^3+1=2\)
\(c.\left(3x-1\right)\left(3x+1\right)-\left(3x-2\right)^2\\ =9x^2-1-\left(9x^2-12x+4\right)\\ =9x^2-1-9x^2+12x-4\\ =12x-5\)
\(d.\left(2x-3\right)^2-\left(2x+3\right)\left(2x-3\right)\\ =\left(2x-3\right)\cdot\left[\left(2x-3\right)-\left(2x+3\right)\right]\\ =\left(2x-3\right)\cdot\left(2x-3-2x-3\right)\\ =\left(2x-3\right)\cdot\left(-6\right)\\ =-12x\cdot18\)
\(e.\left(3x-4\right)^2-\left(2x+4\right)^2\\ =9x^2-24x+16-\left(4x^2+16x+16\right)\\ =9x^2-24x+16-4x^2-16x-16\\ =5x^2-40x\)
\(f.\left(3x-5\right)^3-\left(3x+5\right)^3\\ =27x^3-135x^2+225x-125-\left(27x^3+135x^2+225x+125\right)\\ =27x^3-135x^2+225x-125-27x^3-135x^2-225x-125\\ =-270x^2-250\)
\(g.\left(2x-1\right)^2-\left(3x-1\right)^2\\ =4x^2-4x+1-\left(9x^2-6x+1\right)\\ =4x^2-4x+1-9x^2+6x-1\\ =-5x^2+2x\)
\(h.\left(x-2y\right)\left(x^2+2xy+4y^2\right)+\left(x^3-6y^3\right)\\ =x^3-8y^3+x^3-6y^3\\ =2x^3-14y^3\)
a) ( x - 3 )( x + 3 )( x + 2 ) - ( x - 1 )( x2 - 3 ) - 5x( x + 4 )2 - ( x - 5 )2
= ( x2 - 32 )( x + 2 ) - ( x3 - x2 - 3x + 3 ) - 5x( x2 + 8x + 16 ) - ( x2 - 10x + 25 )
= x3 + 2x2 - 9x - 18 - x3 + x2 + 3x - 3 - 5x3 - 40x2 - 80x - x2 + 10x - 25
= ( x3 - x3 - 5x3 ) + ( 2x2 + x2 - 40x2 - x2 ) + ( -9x + 3x + 10x - 80x ) + ( -18 - 3 - 25 )
= -5x3 - 38x2 - 76x - 46
b) 2x( x - 4 )2 - ( x + 5 )( x - 2 )( x + 2 ) + 2( x + 5 )2 - ( x - 1 )2
= 2x( x2 - 8x + 16 ) - ( x + 5 )( x2 - 4 ) + 2( x2 + 10x + 25 ) - ( x2 - 2x + 1 )
= 2x3 - 16x2 + 32x - ( x3 + 5x2 - 4x - 20 ) + 2x2 + 20x + 50 - x2 + 2x - 1
= 2x3 - 16x2 + 32x - x3 - 5x2 + 4x + 20 + 2x2 + 20x + 50 - x2 + 2x - 1
= ( 2x3 - x3 ) + ( -16x2 - 5x2 + 2x2 - x2 ) + ( 32x + 4x + 20x + 2x ) + ( 20 + 50 - 1 )
= x3 - 20x2 + 58x + 69
c) ( x + 5 )2 - 4x( 2x + 3 )2 - ( 2x - 1 )( x + 3 )( x - 3 )
= x2 + 10x + 25 - 4x( 4x2 + 12x + 9 ) - ( 2x - 1 )( x2 - 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - ( 2x3 - x2 - 18x + 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - 2x3 + x2 + 18x - 9
= ( -16x3 - 2x3 ) + ( x2 - 48x2 + x2 ) + ( 10x - 36x + 18x ) + ( 25 - 9 )
= -18x3 - 46x2 - 8x + 16
d) -2x( 3x + 2 )( 3x - 2 ) + 5( x + 2 )2 - ( x - 1 )( 2x + 1 )( 2x - 1 )
= -2x( 9x2 - 4 ) + 5( x2 + 4x + 4 ) - ( x - 1 )( 4x2 - 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - ( 4x3 - 4x2 - x + 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - 4x3 + 4x2 + x - 1
= ( -18x3 - 4x3 ) + ( 5x2 + 4x2 ) + ( 8x + 20x + x ) + ( 20 - 1 )
= -22x3 + 9x2 + 29x + 19
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) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
a)(3x-1)2+2(3x-1)(2x+1)2(2x+1)=48x^4+56x^3+21x^2-12x-1 cái này tra google
b)(x2+1)(x-3)-(x-3)(x2+3x+9)=(x2+1)(x-3)-(x-3)(x+3)2=(x-3)[(x2+1)-(x+3)2 ]
c)(2x+3)2+(2x+5)2-2(2x+3)(2x+5)=(2x+3)2+(2x+5)2-(2x+3)(2x+5)-(2x+3)(2x+5)=(2x+3)(2x+3-2x+5)+(2x+5)(2x+5-2x+3)
=8(2x+3)+8(2x+5)=8(2x+3+2x+5)
=8(4x+8)
d)(x-3)(x+3)-(x-3)2 =(x-3)(x+3)-(x-3)(x-3)=(x-3)(x+3-x-3)=0
e)(2x+1)2+2(4x2-1)+(2x-1)2 =(2x+1)2+2[(2x)2 -1]+(2x-1)2 =(2x+1)(2x+1+2x-1)+(2x-1)(2x+1+2x-1)=4x(2x+1)+4x(2x-1)
=4x(2x+1+2x-1)=16x2
f)(x2-1)(x+2)-(x-2)(x2+2x+4)= (x2-1)(x+2)-(x-2)(x+2)2 =(x2-1)(x+2)-(x2-22)(x+2)=(x+2)(x2-1-x2-22) mình đoán câu f khai triển ra thế này nhưng kq không giống nhau nên chắc bạn phải tự làm rồi
\(a,VT=\left(a+b+c\right)\left(a-b+c\right)\)
\(=\left(a+c+b\right)\left(a+c-b\right)\)
\(=\left(a+c\right)^2-b^2\)
\(=a^2+2ac+c^2-b^2=VP\)
\(b,VT=\left(3x+2y\right)\left(3x-2y\right)-\left(4x-2y\right)\left(4x+2y\right)\)
\(=9x^2-4y^2-16x^2+4y^2=-7x^2=VP\)
\(c,VT=x^3-1-x^3-1=-2=VP\)
\(d,VT=8x^3+1-8x^3+1=2=VP\)
\(e,VT=\left(x^2+2xy+4y^2\right)\left(x-2y-2x+1\right)\)
\(=\left(x^2+2xy+4y^2\right)\left(-x-2y+1\right)\)
\(=-x^3-2x^2y+x^2-2x^2y-4xy^2+2xy-4xy^2-8y^3+4y^2\)
( bn kiểm tra lại đề nhé)
a) ( 2x + 5 )2 - ( 2x - 5 )2
= [ 2x + 5 + ( 2x - 5 ) ][ 2x + 5 - ( 2x - 5 ) ]
= [ 2x + 5 + 2x - 5 ][ 2x + 5 - 2x + 5 ]
= 4x.10 = 40x
b) ( 4x - 1 )2 - ( x - 1 )( x + 1 )
= 16x2 - 8x + 1 - ( x2 - 1 )
= 16x2 - 8x + 1 - x2 + 1
= 15x2 - 8x + 2
d) ( x + 2 )( x - 2 ) - 2( x2 + 4 ) - ( x2 - 1 )( x2 + 1 )
= x2 - 4 - 2x2 - 8 - ( x4 - 1 )
= x2 - 4 - 2x2 - 8 - x4 + 1
= -x4 - x2 - 11
e) ( 2x + 3 )3 = 8x3 + 362 + 54x + 27
f) ( x2 + 2y )3 = x6 + 6x4y + 12x2y2 + 8y3
g) ( x2 - y/2 )3 = ( x2 - 1/2y )3
= x6 - 3/2x4y + 3/4x2y2 - 1/8y3
Cái chỗ kq phần b) sao đang 16x xuống dưới lại 15x ạ?