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\(x^2+4xy-9+4y^2\)
\(=\left(x^2+4xy+4y^2\right)-9\)
\(=\left(x+2y\right)^2-3^2\)
\(=\left(x+2y+3\right)\left(x+2y-3\right)\)
\(=\left(x+2y\right)^2-9=\left(x+2y-3\right)\left(x+2y+3\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2+4xy-4z^2+4y^2\)
\(=x^2+4xy+4y^2-4z^2\)
\(=\left(x+2y\right)^2-4z^2\)
\(=\left(x+2y-2z\right)\left(x+2y+2z\right)\)
\(x^2+2x-15\)
\(=x^2+2x+1-16\)
\(=\left(x+1\right)^2-16\)
\(=\left(x+1-4\right)\left(x+1+4\right)\)
\(=\left(x-3\right)\left(x+5\right)\)
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1, \(a^6+b^3=\left(a^2+b\right)\left(a^4-a^2b+b^2\right)\)
2, \(x^2-10x+25=\left(x-5\right)^2\)
3, \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
4, \(x^2+4xy+4y^2=\left(x+2y\right)^2\)
1) \(a^6+b^3=\left(a^2\right)^3+b^3=\left(a^2+b\right)\left(a^4-a^2b+b^2\right)\)
2) \(x^2-10x+25=\left(x-5\right)^2\)
3) \(8x^3-\dfrac{1}{8}=\left(2x\right)^3-\left(\dfrac{1}{3}\right)^3=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2x}{3}+\dfrac{1}{4}\right)\)
4) \(x^2+4xy+4y^2=\left(x+2y\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
M = x2 + 4y2 – 4xy
= x2 – 2.x.2y + (2y)2 (Hằng đẳng thức (2))
= (x – 2y)2
Thay x = 18, y = 4 ta được:
M = (18 – 2.4)2 = 102 = 100
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\(2x^2-4xy+2y^2\\ =2\left(x^2-2xy+y^2\right)\\ =2\left(x-y\right)^2\)
a) 2x2-4xy+2y2
= 2x2-2xy-2xy+2y2
= 2x(x-y)-2y(x-y)
= (2x-2y)(x-y)
b) x2+4xy+4y2-9
= (x+2y)2-32
= (x+2y-3)(x+2y+3)
c) x4-x3y+x-y
= x3(x-y)+(x-y)
= (x3+1)(x-y)
\(x^2+4y^2-4xy-4\)
\(=\left(x^2-4xy+4y^2\right)-4\)
\(=\left(x-2y\right)^2-2^2\)
\(=\left(x-2y-2\right)\left(x-2y+2\right)\)