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x2-7x+12
=x2-3x-4x+12
=x(x-3)-4(x-3)
=(x-3)(x-4)
x4-4x2+4x-1
=x4-1-4x2+4x
=(x2-1)(x2+1)-4x(x-1)
=(x-1)(x+1)(x2+1)-4x(x-1)
=(x-1)[(x+1)(x2+1)-4x]
=(x-1)(x3+x2+x+1-4x)
=(x-1)(x3+x2-3x+1)
6x4-11x2+3
=6x4-2x2-9x2+3
=2x2(3x2-1)-3(3x2-1)
=(3x2-1)(2x2-3)
1. x2 + 2xy + y2 - xz - yz
= ( x2 +2xy + y2 ) - z ( x + y )
= ( x + y )2 - z ( x + y )
= ( x + y ) [( x + y ) - z ]
= ( x + y ) ( x + y - z )
1 x^2+2xy+y^2-xz-yz
=(x+y)^2-z(x+y)
=(x+y)(x+y-z)
2 (7x^2-14xy+7^2)-29z^2
=7(x^2-2xy+1)-29z^2
=7(x-1)^2-29z^2
=7(x-1)^2-25z^2-7z^2
=7(x-1-5)(x-1+5)-7z^2
=7(x-6)(x+4)-7z^2
=7((x+6)(x+4)-z^2)
3 5x^3-5x^2y+10x^2-10xy
=5x(x^2-xy+2x-2y)
4 5x^2-10xy+5y^2-20z^2
=5(x^2-2xy+y^2)-20z^2
=5(x+y)^2-20z^2
=5((x+y)^2-4z^2)
=5((x+y-2z)(x+y+2z))
a)
\(10x^2+10xy+5x+5y\)
\(=10x\left(x+y\right)+5\left(x+y\right)\)
\(=5\left(x+y\right)\left(2x+1\right)\)
b)
\(x^3+x^2-x-1\)
\(=x^2\left(x+1\right)-\left(x+1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
c)
\(x+2a\left(x-y\right)-y\)
\(=\left(x-y\right)+2a\left(x-y\right)\)
\(=\left(x-y\right)\left(2a+1\right)\)
d)
\(x^2-y^2+7x-7y\)
\(=\left(x+y\right)\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+1\right)\)
- x2.(x3-x2+x-1)
- x.( x3-3x2-1)+3
- x.(x2-xy-y2)
Tìm x:
x3-16x = 0
=> x.(x2-16) = 0
=> x = 0 hay x2-16 = 0
=> x = 0 hay x2 = 0+16
=> x = 0 hay x2 = 16
=> x = 0 hay x = 4 hay x = -4
\(x^3-4x^2-8x+8\)
\(\Leftrightarrow\left(x^3-4x^2\right)-\left(8x-8\right)\)
\(\Leftrightarrow x^2\left(x-4\right)-4\left(x-4\right)\)
\(\Leftrightarrow\left(x-4\right)\left(x^2-4\right)\)
\(x^3+2x-3\)
\(=x^3-x+3x-3\)
\(=x\left(x^2-1\right)+3\left(x-1\right)\)
\(=x\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x\left(x+1\right)+3\right)\)
\(x^3+5x^2+8x+4\)
\(=\left(x+1\right)\left(x+2\right)\)
Cây cuối tương tự câu đầu thôi:
\(x^3-7x+6\)
\(=x^3-x-6x+6\)
.......
x4+x=x(x3+1)=x(x+1)(x2-x+1)
x4+64=x4+16x2+64-16x2=(x2+8)2-(4x)2=(x2+8+4x)(x2+8-4x)
4x4+81=4x4+36x2+81-36x2=(2x2+9)2-(6x)2=(2x2+9+6x)(2x2+9-6x)
64x4+y4=64x4+16(xy)2+y4-16(xy)2=(8x2+y2)-(4xy)2=(8x2+y2-4xy)(8x2+y2=4xy)
x4+4y4=x4+4(xy)2+4y4-4(xy)2=(x2+2y2-2xy)(x2+2y2+2xy)
x4+x2+1=(x4+2x2+1)-x2=(x2+1-x)(x2+1+x)
Mình làm có vài đoạn hơi tắt nha.
+,
= (x-y)^2 - z.(x-y) = (x-y).(x-y-z)
+,
=(x-y).(x+y)-(x-y) = (x-y).(x+y-1)
+,
=x^3.(x-1)-(x^2-1) = x^3.(x-1).(x-1).(x+1) = (x-1).(x^3-x-1)
+,
=a.(x^2-y^2)-7.(x+y) = a.(x+y).(x-y)-7.(x+y) = (ax+ay-7).(x+y)
\(x^2-2xy+y^2-xz+yz\)
\(=\left(x-y\right)^2-\left(xz-yz\right)\)
\(=\left(x-y\right)\left(x-y\right)-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
\(x^2-y^2-x+y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
\(x^4-x^3-x^2+1\)
\(=x^3\left(x-1\right)-\left(x^2-1\right)\)
\(=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
\(ax^2-ay^2-7x-7y\)
\(=a\left(x^2-y^2\right)-\left(7x+7y\right)\)
\(=a\left(x-y\right)\left(x+y\right)-7\left(x-y\right)\)
\(=\left(x-y\right)\left[a\left(x+y\right)-7\right]\)