Question

a) Simplify: (a + b + c) (a - b -c) (a+b)​

Answer 1

Answer :

$\longmapsto\sf(a + b + c)(a - b - c)(a + b) \\\\ \longmapsto\sf a(a - b - c) + b(a - b - c) + c(a - b - c)(a + b) \\\\ \longmapsto\sf (a {}^{2} - ab - ac + ab - b {}^{2} - bc + ac - bc - c {}^{2})(a + b) \\\\ \longmapsto\sf (a {}^{2} - b {}^{2} - c {}^{2} - 2bc)(a + b) \\\\ \longmapsto\sf a(a {}^{2} - b {}^{2} - c {}^{2} - 2bc) + b(a {}^{2} - b {}^{2} - c {}^{2} - 2bc) \\\\ \longmapsto\bold{ a {}^{3} - ab {}^{2} - ac {}^{2} - 2abc + a {}^{2}b - b {}^{3} - bc {}^{2} - 2b {}^{2}c }$

Answer 2

Answer:

$\boxed{(a^3 -2abc - ab^2 -ac^2 + a^2b - 2b^2c - b^3 -bc^2)}$

Step-by-step explanation:

$(a+b+c)(a-b-c)(a+b)\\\\= (a^2 -ab -ac + ab - b^2 -bc + ac - bc - c^2)(a+b)\\\\= (a^2 -2bc -b^2 - c^2)(a+b)\\\\= \boxed{(a^3 -2abc - ab^2 -ac^2 + a^2b - 2b^2c - b^3 -bc^2)}$