Question

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

Answer 1

=56

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