Răspuns:
Explicație pas cu pas:
12.
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
a)
(√2 + √3)^2 + (√2 - √3)^2
= 2 + 2√6 + 3 + 2 - 2√6 + 3
= 10
b)
(√2 - √5)^2 - (√2 - √5)^2 = 0
_______________
13.
a)
(√3 + √5x)^2 - (√15x - 2)^2
= 3 + 2x√15 + 5x^2 - (15x^2 - 4x√15 + 4)
= 3 + 2x√15 + 5x^2 - 15x^2 + 4x√15 - 4
= -10x^2 + 6x√15 - 1
b)
(3 - √14x)^2 - (√7x + √2)^2
= 9 - 6x√14 + 14x^2 - (7x^2 + 2x√14 + 2)
= 9 - 6x√14 + 14x^2 - 7x^2 - 2x√14 - 2
= 7x^2 - 8x√14 + 7
_________________
14.
(a - b)(a + b) = a^2 - b^2
a)
(x - 5)(x + 5)(x^2 + 25) = (x^2 - 25)(x^2 + 25) = x^4 - 625
b)
(x - 4)(x + 4)(x^2 + 16) = (x^2 - 16)(x^2 + 16) = x^4 - 256
