Question

Calculați,folosind formulele de calcul prescurtat :
(5x - 2) la 2 =
( a√3 + b√2 ) la 2 =
(x-2) (x+2)=
(a pe √5 - b) (a pe √5 + b)=
(2x + 1) la 2 - ( x+6) (x-6) - 3(x-2 ) la 2 =

Answer 1

$(5x-2)^2=(5x)^2-2*5x*2+2^2=25x^2-20x+4 \\ (a \sqrt{3} +b \sqrt{2} )^2=(a \sqrt{3} )^2+2*a \sqrt{3} *b \sqrt{2} +(b \sqrt{2} )^2=3a^2+2ab \sqrt{6} +2b^2 \\ (x-2)(x+2)=x^2-4 \\ ( \frac{a}{ \sqrt{5} }-b)( \frac{a}{ \sqrt{5} }+b ) = \frac{a^2}{5} -b^2 \\ (2x+1)^2-(x+6)(x-6)-3(x-2)^2= \\ =(2x)^2+2*2x*1+1^2-x^2+36-3(x^2-2*x*2+2^2)= \\ =4x^2+4x+1-x^2+36-3(x^2-4x+4)= \\ =4x^2+4x+1-x^2+36-3x^2+12x-12=16x+25$