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![](https://rs.olm.vn/images/avt/0.png?1311)
A= (6x-2)^2 + (2-5x)^2+2(6x-2)(2-5x)
= (6x-2)^2 +2(6x-2)(2-5x)+ (2-5x)^2
\(=\left(6x-2+2-5x\right)^2=x^2\)
B= (2a^2+2a+1)(2a^2-2a+1)-(2a^2+1)^2
\(=\left(2a^2+1\right)^2-4a^2-\left(2a^2+1\right)^2=4a^2\)
C=(x+3)(x^2-3x+9)-(54+x^3)
\(=\left(x^3+27\right)-54-x^3=27\)
D=(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)
\(=\left(2x+y\right)^3-\left(2x-y\right)^3\)
E=(a+b)^2-(a-b)^2
\(=\left(a+b+a-b\right)\left(a+b-a+b\right)=2a.2b=4ab\)
Secret Personv: thật.CTV lạ z
\(C=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3-27-54-x^3=-81\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2: Rút gọn biểu thức sau một cách nhanh nhất:
a, A=(6x-2)2+(2-5x)2+2.(6x-2)(2-5x)
\(=\left(6x-2\right)^2+2\left(6x-2\right)\left(2-5x\right)+\left(2-5x\right)^2\)
\(\text{(Hằng đẳng thức số 2)}\)
\(=\left(6x-2+2-5x\right)\)
\(=x\)
\(B=\left(2a^2+2a+1\right)\left(2a^2-2a+1\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1+2a\right)\left(2a^2+1-2a\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1\right)^2-4a^2-\left(2a^2+1\right)^2\)
\(=-4a^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) A=(4-5x)2-(3+5x)2=(4-5x-3-5x)(4-5x+3+5x)=(-25x+1)1=-25x+1
B=(3x-1)(1+3x)-(3x+1)2=9x2-1-(3x+1)2=9x2-1-(9x2+6x+1)=9x2-1-9x2-6x-1=-6x-2=-2(3x+1)
a) \(\left(\left(6x-2\right)+\left(2-5x\right)\right)^2=x^2\)
b) \(\left(\left(2a^2+1\right)+2a\right)\left(\left(2a^2+1\right)-2a\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1\right)^2-1-\left(2a^2+1\right)^2\)
\(=-1\)