Question

solve
${(a + b + c)}^{3}$
give step by step explanation please ​

Answer 1

We know that

(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3

(a + b + c)^3

= [(a + b) + c]^3

= (a + b)^3 + 3*(a + b)^2*c + 3*(a + b)*c^2 + c^3

= (a + b)^3 + 3*(a^2 + 2ab + b^2) + 3*a*c^2 + 3*b*c^2 + c^3

= (a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 3*(a^2 + 2ab + b^2) + 3*a*c^2 + 3*b*c^2 + c^3

= a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 3*a^2 + 6*a*b + 3*b^2 + 3*a*c^2 + 3*b*c^2 + c^3

= a^3 + b^3 + c^3 + 3*a^2*b + 3*a*b^2 + 3*a*c^2 + 3*b*c^2 + 3*a^2 + 3*b^2 + 6*a*b ——> Answer