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Phân tích thành nhân tử:
(4x + 3y)2 + (6xy - 2)2
=\((16x^2+24xy+9y^2)+(36x^2y^2-24xy+4)\)
=\(16x^2+24xy+9y^2+36x^2y^2-24xy+4\)
=\(16x^2+9y^2+36x^2y^2+4\)
=\((4x)^2+(3y)^2+(6xy)^2+2^2\)
MÌNH CHỈ LÀM ĐC TỚI ĐÂY
a) 16(4x+5)2 - 25(2x+2)2
\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)
\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)
\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)
\(=\left(26x+30\right)\left(6x+10\right)\)
\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-2y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-3y+5\right)\)
\(c,\left(x+1\right)^4-\left(x-1\right)^4\)
\(=\left(x+1\right)^{2^2}-\left(x-1\right)^{2^2}\)
\(=\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\)
\(=\left(x^2+2x+1+x^2-2x+1\right)\left[\left(x+1+x-1\right)\left(x+1-x+1\right)\right]\)
\(=\left(2x^2+2\right)2x.2\)
\(=4x.2\left(x^2+1\right)\)
\(=8x\left(x^2+1\right)\)
\(x^6-y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
hk
tốt
8x3 - 27y3 = 23 . x3 - 33 . y3 = ( 2x )3 - ( 3y )3 = ( 2x - 3y ) [(2x)2 + 12xy + (3y)2 ].
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b-2a-a\right)\left(2a+b+2a+a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)
\(\left(2a+b\right)^2-\left(2a+a\right)^2\)
\(=\left(2a+b\right)^2-\left(3a\right)^2\)
\(=\left(2a+b-3a\right)\left(2a+b+3a\right)\)
\(=\left(b-a\right)\left(5a+b\right)\)
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a/ 2x^3 -5x^2 + 8x -3
= 2x^3 -x^2 -4x^2 +2x +6x -3
= x^2 .[2x-1] - 2x[2x-1] +3. [2x-1]
= [x^2-2x+3] [2x-1]
b/ 3x^3 - 14x^2 +4x +3
= 3x^3 +x^2 -15 x^2 -5x +9x +3
= x^2 [3x+1] -5.x [3x+1] +3. [3x+1]
= [x^2 -5x+3] [3x+1]
c/ Đặt C = 12x^2 + 5 x -12 y^2 +12y -10xy -3
= -[12y^2+10xy+3-12x^2-5x-12y]
12y^2 + 10xy +3-12x^2-5x-12y = 18xy +12y^2 -6y - 12x^2 -8xy +4x -9x -6y +3
= 6y [3x+2y-1] - 4.x[3x+2y-1] -3.[3x+2y-1]
= [6y-4x-3] [3x+2y-1]
=> C = -[6y-4x-3]. [ 3x+2y-1]
tom lai minh ra
12x2+5x-12y2+12y-10xy-3=12(x+(2y-1)/3)(x-(6y-3)/4)) co dung ko nha.
(a - b)3 - (b - a)2 + b(a - b)2
= (a - b)3 - ( a-b ) 2 + b( a-b ) 2
= ( a-b )2 . ( a - b - 1 + b )
= ( a2 - 2ab + b2 ) (a - 1 )
vậy ....
Mình không chắc là đúng đâu nhé