Question

A pupil wrote:

for all numbers j and k,
(j+k)² = j² + k²
Expand and simplify (j+k)² to show that the pupil is wrong.

Answer 1

see explanation

Explanation:

(j + k)²

= (j + k)(j + k)

each term in the second factor is multiplied by each term in the first factor , that is

j(j + k) + k(j + k) ← distribute parenthesis

= j² + jk + jk + k² ← collect like terms

= j² + 2jk + k²