Question

Aduceti expresia la forma cea mai simpla:
a)(a-√2)²-(a+√2)²+3√2
b)a²-2ab+b²/a-b +a+b
c)x²-4y²-x+2y -2y
d)(√5-x)²+(x+√5)²-4√5
e)(a-2x)²-4x²-a²

Answer 1

[tex]a)(a-\sqrt{2})^2-(a+\sqrt2)^2+3\sqrt2=\\ a^2-2a\sqrt2+2-a^2-2a\sqrt2-2+3\sqrt2=\\ -4a\sqrt2+3\sqrt2=\sqrt2(3-4a)\\ b)\frac{a^2-2ab+b^2}{a-b}+a+b=\\ \frac{(a-b)^2}{a-b}+a+b=\\ a-b+a+b=2a\\ c)x^2-4y^2-x+2y-2y=\\ x^2-4y^2-x=\\ (x-2y)(x+2y)-x=\\ d)(\sqrt5-x)^2+(x+\sqrt5)^2-4\sqrt5=\\ 5-2x\sqrt5+x^2+x^2+2x\sqrt5+5-4\sqrt5=\\ 10+2x^2-4\sqrt5=\\ 2(x^2-2\sqrt5+5)=\\ 2(x-\sqrt5)^2\\ e)(a-2x)^2-4x^2-a^2= a^2-4ax+4x^2-4x^2-a^2=-4ax [/tex]