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[(a−b)(c−b)+(b−a)(c−a)]+[(b−a)(c−a)+(b−c)(a−c)]+[(b−c)(a−c)+(a−b)(c−b)][(a−b)(c−b)+(b−a)(c−a)]+[(b−a)(c−a)+(b−c)(a−c)]+[(b−c)(a−c)+(a−b)(c−b)]
= [(a−b)(c−b−c+a)]+[(c−a)(b−a−b+c)]+[(b−c)(a−c−a+b)][(a−b)(c−b−c+a)]+[(c−a)(b−a−b+c)]+[(b−c)(a−c−a+b)]
= (a−b)2+(c−a)2+(b−c)2
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) \(a^2-6a+9=\left(a-3\right)^2\)
b) \(\dfrac{1}{4}x^2+2xy^2+4y^4=\left(\dfrac{1}{2}x+2y^2\right)^2\)
Bài 2:
a) \(\Leftrightarrow-9x^2+30x-25+9x^2+18x+9=30\)
\(\Leftrightarrow48x=46\Leftrightarrow x=\dfrac{23}{24}\)
b) \(\Leftrightarrow x^2+8x+16-x^2+1=16\)
\(\Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\)
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a) \(4x^2+12xy+9y^2\)
\(=\left(2x\right)^2+2.2x.3+\left(3y\right)^2\)
\(=\left(2x+3y\right)^2\)
b) \(81x^2-18xy+y^2\)
\(=\left(9x\right)^2-2.9x.y+y^2\)
\(=\left(9x-y\right)^2\)
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\(2xy^2+x^2y^4+1\\ =\left(xy^2\right)^2+2xy^2.1+1^2\\ =\left(xy^2+1\right)^2\)
Ta có :
\(2xy^2+x^2y^4+1=\left(xy^2\right)^2+2.xy^2.1+1^2\)
\(=\left(xy^2+1\right)^2\)
= ( xy^2 + 1 )^2