Question

Efectuati ,utilizand formulele de calcul prescurtat:
a) ( radical din 2 + x) la puterea 2
b) ( x + 2 radical din 2) la puterea 2
c) (1/4 + a) la puterea 2
d) (3x/2 + 1) la puterea 2
e) (1/3x + 2/5y) la puterea 2
f) (x + 2 radical 5) la puterea 2
g) (radical 2a + 1/radical 3 b) la puterea 2​

Answer 1

$a) \: {( \sqrt{2} + x)}^{2} = { \sqrt{2} }^{2} + 2 \times \sqrt{2} \times x + {x}^{2} = 2 + 2x \sqrt{2} + {x}^{2} \\ b) \: {(x + 2 \sqrt{2}) }^{2} = {x}^{2} + 4x \sqrt{2} + 8 \\ c) \: \: {( \frac{1}{4} + a)}^{2} = \frac{1}{16} + \frac{2a}{4} + {a \: }^{2} = \frac{1}{16} + \frac{a}{2} + {a}^{2} \\ d) \: {( \frac{3x}{2} + 1) }^{2} = \frac{ {9x}^{2} }{4} + 3x + 1 \\ e) \: {( \frac{1}{3x} + \frac{2}{5y}) }^{2} = \frac{1}{ {9x}^{2} } + \frac{5}{15xy} + \frac{4}{ {20y}^{2} } \\ f) \: {(x + 2 \sqrt{5} )}^{2} = {x}^{2} + 4x \sqrt{5} + 20 \\ g) {( \sqrt{2a} + \frac{1}{ \sqrt{3b} } ) }^{2} = 2a + \frac{2 \sqrt{2a} }{ \sqrt{3b} } + \frac{1}{3b}$

Sper ca te-am ajutat ( vezi ca mai poti simplifica/rationaliza la unele)