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\(a,\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)
\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)
x2 - 2xy + y2 - x2
= (x - y)2 - x2
= (x - y -x) (x - y + x)
= -y(2x -y)
x2 - 2xy - 4x2 + y2
= (x2 - 2xy + y2) - 4x2
= (x - y)2 - 4x2
= (x - y - 2x)(x - y +2x)
(2x + 1 )2 - ( x - 1)2
= (2x + 1 - x + 1)(2x + 1 + x - 1)
= 3x( x + 2)
4a2 - 4a + 1
= (2a - 1)2
-9x2 + 6xy - y2
= - (9x2 - 6xy + y2)
= - (3x - y)2
-6x + 9 + x2
= x2 - 6x + 9
= (x - 3)2
4x2 - 4x + 1 - y2
= (2x - 1)2 - y2
= (2x - 1 - y2)(2x - 1 + y2)
a)\(\left(2x-y\right)[\left(2x\right)^2-2.2x.y+y^2]\)
\(=\left(2x-y\right)^3\)
b)\(2x^2-3xy+5y^2\)
c)\(2x^3-10x^2-11x^2+55x+12x-60\)
\(=2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\)
\(=\left(x+5\right)\left(2x^2-11x+12\right)\)
\(\Leftrightarrow(2x^3-21x^2+67x-60)/\left(x-5\right)=2x^2-11x+12\)
1) x2 - 2xy + y2 - x2
=(x - y)2 - x2
=(x - y - x)(x - y + x)= -y(2x - y)
2) x2 - 2xy - 4z2 + y2
= x2 - 2xy + y2 - 4z2
= (x - y)2 - (2z)2 = (x - y - 2z)(x - y + 2z)
3) (2x + 1)2 - (x - 1)2
=(2x + 1 - x + 1)(2x + 1 + x - 1)=3x(x + 2)
4) 4a2 - 4a + 1=(2a - 1)2
5) -9x2 + 6xy - y2
= - (9x2 - 6xy + y2)= - (3x - y)2
6) -6x + 9 + x2
= x2 - 6x + 9 = (x - 3)2
7) 4x2 - 4x + 1 - y2
= (2x - 1)2 - y2 = (2x - 1 - y)(2x - 1 + y)
pn kt lại nha
a)x2-4x+5+y2+2y=x2-4x+4+y2+2y+1=(x-2)2+(y+1)2
b)2x2+y2-2xy+10x+25=x2-2xy+y2+x2+10x+25=(X+Y)2+(X+5)2
c)a2+2ab+5b2+4b+1=a2+2ab+b2+4b2+4b+1=(a+b)2+(2b+1)2
d)2x2+2b2+4x+4b+4=2x2+4x+2+2b2+4b+2=(\(\sqrt{2}x+\sqrt{2}\))2+(\(\sqrt{2}b+\sqrt{2}\))2
e)X4+13-6x2+4y+y2=x4-6x2+9+y2+4y+4=(x2-3)2+(y+2)2
f)-6x+9x2-8y+4y+y2+5= 9x2-6x+1+4y2-8y+4= (3x-1)2+(2y-2)2
a/ \(\left(x^2+y^2\right)^2-4x^2y^2=\left(x^2+y^2\right)^2-\left(2xy\right)^2=\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)=\left(x+y\right)^2\left(x-y\right)^2\)
b/ \(x^2y^2-\left(14y\right)^2=\left(xy-14y\right)\left(xy+14y\right)\)
c/ \(25-x^2+2xy-y^2=25-\left(x^2-2xy+y^2\right)=25-\left(x-y\right)^2=\left(5-x+y\right)\left(5+x-y\right)\)
d/ \(9x^2-x^2+6x=8x^2+6x=2x\left(4x+3\right)\)