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1:
a: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2zx+2yz\)
b: \(\left(x-y+z\right)^2=x^2+y^2+z^2-2xy+2xz-2yz\)
c: \(\left(x-y-z\right)^2=x^2+y^2+z^2-2xy-2xz+2yz\)
a) \(\left(\left(6x-2\right)+\left(2-5x\right)\right)^2=x^2\)
b) \(\left(\left(2a^2+1\right)+2a\right)\left(\left(2a^2+1\right)-2a\right)-\left(2a^2+1\right)^2\)
\(=\left(2a^2+1\right)^2-1-\left(2a^2+1\right)^2\)
\(=-1\)
a) \(ĐKXĐ:a\ne\pm1\)
b) \(P=\left(\dfrac{a+1}{2a-2}+\dfrac{1}{2-2a^2}\right)\cdot\dfrac{2a+2}{a+2}\)
\(=\left(\dfrac{a+1}{2\left(a-1\right)}+\dfrac{1}{2\left(1-a^2\right)}\right)\cdot\dfrac{2\left(a+1\right)}{a+2}\)
\(=\left(\dfrac{a+1}{2\left(a-1\right)}-\dfrac{1}{2\left(a-1\right)\left(a+1\right)}\right)\cdot\dfrac{2\left(a+1\right)}{a+2}\)
\(=\dfrac{\left(a+1\right)\left(a-1\right)-1}{2\left(a-1\right)\left(a+1\right)}\cdot\dfrac{2\left(a+1\right)}{a+2}\)
\(=\dfrac{a^2-1-1}{\left(a-1\right)\left(a+2\right)}\)
\(=\dfrac{a^2-2}{a^2+a-2}\)
Khi a = 2 thì :
\(P=\dfrac{2^2-2}{2^2+2-2}=\dfrac{2}{4}=\dfrac{1}{2}\)
p/s: check lại hộ tui nhá =)))
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+1/2a-2-1/2a^2)2a+2/a+2
=2a^2+5/2a^2-4a-5/2a^3+2/a+2
=-5/2a^3+9/2a^2-2a+2
(a+1/2a-2-1/2a^2)2a+2/a+2
=2a^2+5/2a^2-4a-1/2a^3+2/a+2
=-1/2a^3+9/2a^2-4a+2/a+2