Use the Binomial theorem to expand and where possible simplify the expression. (1+√3) ^4 + (1-√3) ^4

=56

Step-by-step explanation:

Binomial theorem: (x+y) = x²+2xy+y² or (x-y) = x² - 2xy+y²

(1+√3) ⁴ + (1-√3) ⁴ = ((1+√3) ²) ² + ((1-√3) ²) ² = (1+2√3+3) ² + (1-2√3+3) ²=

= (4+2√3) ² + (4-2√3) ² = (16+16√3+12) + (16 - 16√3+12) = 28+16√3+28-16√3=56