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\(a,=xy\left(-6x+y\right)\)
\(b,=10c\left(a^2-9b^2+3bc-ac\right)=10c\left[\left(a-3b\right)\left(a+3b\right)-c\left(a-3b\right)\right]\)
\(=10c\left[\left(a-3b\right)\left(a+3b-c\right)\right]\)
c,\(=a\left(x-c\right)-b\left(x-c\right)=\left(a-b\right)\left(x-c\right)\)
d,\(=-\left(x-2y-6\right)\left(x-2y+6\right)\)
e;\(=m^2+4m+mn+n^2+4n+mn=m\left(m+4+n\right)+n\left(m+4+n\right)\)\(=\left(m+n\right)\left(m+n+4\right)\)
f,\(=\dfrac{1}{2}\left(4x^2-y^2\right)=\dfrac{1}{2}\left(2x-y\right)\left(2x+y\right)\)
\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)
\(=3\left(a-b+c\right)\left(x+6y\right)^2\)
___________________
\(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
\(=\left(y+4\right)^2-9x^2=\left(y-3x+4\right)\left(y+3x+4\right)\)
a) Sửa đề: \(x^2+3x+1\rightarrow x^2+2x+1\)
\(x^2+2x+1=\left(x+1\right)^2\)
b) \(x^2+y^2+2xy=\left(x+y\right)^2\)
c) \(9x^2+12x+4=\left(3x+2\right)^2\)
d) \(-4x^2-9-12x=-\left(4x^2+12x+9\right)=-\left(2x+3\right)^2\)
\(a,5\left(x-y\right)-3x\left(y-x\right)=5\left(x-y\right)+3x\left(x-y\right)=\left(5+3x\right)\left(x-y\right)\\ b,x^2-4xy+4y^2=\left(x-2y\right)^2\\ c,\left(x+1\right)^2+x\left(5-x\right)=0\\ \Rightarrow x^2+2x+1+5x-x^2=0\\ \Rightarrow7x+1=0\\ \Rightarrow7x=-1\\ \Rightarrow x=-\dfrac{1}{7}\)
a: =(x-y)(5+3x)
c: \(\Leftrightarrow x^2-2x+1+5x-x^2=0\)
hay x=-1/3
\(=m^2-\left(n-2\right)^2=\left(m-n+2\right)\left(m+n-2\right)\)
b:=y^2+2y+1+9x^2-12x+4
=(y+1)^2+(3x-2)^2
a:
SỬa đề: 5y^2
=y^2-10y+25+9x^2+4y^2-12xy
=(y-5)^2+(3x-2y)^2
\(a,Sửa:16-9x^2+y^2-8y\\ =\left(y-4\right)^2-9x^2\\ =\left(y-3x-4\right)\left(y+3x-4\right)\\ b,=\left(n^2+4n\right)^2+10\left(n^2+4n\right)+25\\ =\left(n^2+4n+5\right)^2\)