Question

Simplify and factorise (a + b + c)² - (a - b - c)² + 4b² - 4c²

Answer 1

Given (a + b + c)^2 - (a - b - c)^2 + 4b^2 - 4c^2
= > a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - (a^2 + b^2 + c^2 - 2ab + 2bc - 2ca) + 4b^2 - 4c^2
= > a^2 + b^2 +c^2 + 2ab + 2bc + 2ca - a^2 - b^2 - c^2 + 2ab - 2bc + 2ca + 4b^2 - 4c^2
= > 4ab + 4ac + 4b^2 - 4c^2
= > 4a(b + c) + 4(b + c)(b - c)
= > 4(b + c)(a + b - c)