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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
\(C=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3-27-54-x^3=-81\)
Bài 2: Rút gọn biểu thức sau một cách nhanh nhất:
a, A=(6x-2)2+(2-5x)2+2.(6x-2)(2-5x)
\(=\left(6x-2\right)^2+2\left(6x-2\right)\left(2-5x\right)+\left(2-5x\right)^2\)
\(\text{(Hằng đẳng thức số 2)}\)
\(=\left(6x-2+2-5x\right)\)
\(=x\)
\(B=\left(2a^2+2a+1\right)\left(2a^2-2a+1\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1+2a\right)\left(2a^2+1-2a\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1\right)^2-4a^2-\left(2a^2+1\right)^2\)
\(=-4a^2\)
a) (2a2+2a+1).(2a2-2a+1)-(2a2+1)2
Áp dụng hằng đẳng thức A2- B2= (A+B)(A-B)
ta có : (2a2+1)2 - (2a)2 - (2a2+1)2
= 4a2
a: \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
\(=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\)
\(=\frac{3x-x+6}{2x\left(x+3\right)}=\frac{2x+6}{2x\left(x+3\right)}=\frac{1}{x}\)
b: \(\frac{4a^2-3a+5}{a^3-1}-\frac{1-2a}{a^2+a+1}+\frac{2}{a-1}\)
\(=\frac{4a^2-3a+5+\left(2a-1\right)\left(a-1\right)+2\left(a^2+a+1\right)}{\left(a-1\right)\left(a^2+a+1\right)}\)
\(=\frac{4a^2-3a+5+2a^2-3a+1+2a^2+2a+2}{\left(a-1\right)\left(a^2+a+1\right)}=\frac{8a^2-4a+8}{\left(a-1\right)\left(a^2+a+1\right)}\)
a) \(\left(\left(6x-2\right)+\left(2-5x\right)\right)^2=x^2\)
b) \(\left(\left(2a^2+1\right)+2a\right)\left(\left(2a^2+1\right)-2a\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1\right)^2-1-\left(2a^2+1\right)^2\)
\(=-1\)