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1) \(x^3-x+y^3-y\)
\(=\left(x^3+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
2)\(3x^2+6xy+3y^2-3z^2=3\left(x^2+2xy+y^2-z^2\right)\)
\(=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y-x\right)\left(x+y+z\right)\)
3)\(x^3+y^3-3x-3y=\left(x+y\right)\left(x^2-xy+y^2\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-3\right)\)
\(1.x^3+y^3-x-y=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
2.\(3\left(x^2+6xy+y^2-z^2\right)=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y+z\right)\left(x+y-z\right)\)
3.\(\left(x+y\right)\left(x^2-xy+y^2\right)-3\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2-3\right)\)
cho mình nha
=(5a2+5b2+10ab)-5c2=5.(a2+2ab+b2)-5c2=5.(a+b)2-5c2=5.[(a+b)2-c2]=5.(a+b+c).(a+b-c)
=(5a2+5b2+10ab)-5c2=5.(a2+2ab+b2)-5c2=5.(a+b)2-5c2=5.[(a+b)2-c2]=5.(a+b+c).(a+b-c)
Bài làm:
a) \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(\left(x-y\right)\left(x-y-z\right)\)
a/ \(x^2-2xy+y^2-zx+yz.\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c/ \(x^2-y^2-2x-2y.\)
\(=x^2-2x+1-y^2-2y-1\)
\(=\left(x^2-2x+1\right)-\left(y^2+2y+1\right)\)
\(=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-1+y+1\right)\left(x-1-y-1\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
a) = pq(pm+1 - pm - pq2n+3)
b) = (m-3)2 - (x - 2y)2
= ( m-3 +x -2y)(m-3 -x +2y)
xin lỗi mình chép sai đề, mình vừa mới sửa lại phiền bạn làm lại giùm mình
Đề sai nhé .Sửu lại
\(x^2-4x^2y^2+4+4x\)
\(=\left(x^2+4x+4\right)-4x^2y^2\)
\(=\left(x+2\right)^2-\left(2xy\right)^2\)
\(=\left(x+2+2xy\right)\left(x+2-2xy\right)\)
a) x^2+4x-y^2+4=(x^2+4x+4)-y^2=(x+2)^2-y^2=(x+2-y)(x+2+y)
b)3x^2+6xy+3y^2-3z^2=3[(x^2+2xy+y^2)-z^2]=3[(x+y)^2-z^2]=3(x+y-z)(x+y+z)
a) = (x^2 + 2.2.x + 2^2) - y^2 = (x + 2)^2 - y^2 =(x + 2 - y) . (x + 2 +y)
a)
\(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(x^2+1\right)\left(2x+3\right)\)
b)
\(=a\left(a-b\right)+a-b\)
\(=\left(a+1\right)\left(a-b\right)\)
c)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
d)
\(=x^3\left(x-2\right)+10x\left(x-2\right)\)
\(=x\left(x^2+10\right)\left(x-2\right)\)
e)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
f)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right)\left(x+y\right)\)
a,2x3+3x2+2x+3
=(2x3+2x)+(3x2+3)
=2x(x2+1)+3(x2+1)
=(x2+1)(2x+3)
b,a2-ab+a-b
=(a2-ab)+(a-b)
=a(a-b)+(a-b)
=(a-b)(a+1)
c,2x2+4x+2-2y2
=2(x2+2x+1-y2)
=2[(x2+2x+1)-y2 ]
=2[(x+1)2-y2 ]
=2(x+1-y)(x+1+y)
d,x4-2x3+10x2-20x
=(x4-2x3)+(10x2-20x)
=x3(x-2)+10x(x-2)
=(x-2)(x3+10x)
=(x-2)[x(x2+10)]
e,x3+2x2+x
=x(x2+2x+1)
=x(x+1)2
f,xy+y2-x-y
=(xy+y2)-(x-y)
=y(x+y)-(x+y)
=(x+y)(y-1)
1) Ta có: \(3x^2-6xy+3y^2-3z^2\)
\(=3\left(x^2-2xy+y^2-z^2\right)\)
\(=3\left[\left(x^2-2xy+y^2\right)-z^2\right]\)
\(=3\left[\left(x-y\right)^2-z^2\right]\)
\(=3\left(x-y-z\right)\left(x-y+z\right)\)
2) Ta có: \(5a^2+10ab+5b^2-5c^2\)
\(=5\left(a^2+2ab+b^2-c^2\right)\)
\(=5\left[\left(a^2+2ab+b^2\right)-c^2\right]\)
\(=5\left[\left(a+b\right)^2-c^2\right]\)
\(=5\left(a+b-c\right)\left(a+b+c\right)\)