[tex](a + b) {}^{3} = a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} \\ \\ x {}^{6} + 6x {}^{4} y + 12x {}^{2} y {}^{2} + 8y {}^{3} [/tex]
Answer:
x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.
Step-by-step explanation:
Using the Binomial Theorem:
(x^2 + 2y)^3 = (x^2)^3 + 3C1 (x^2)^2 (2y) + 3C2 x^2 (2y)^2 + (2y)^3
= x^6 + 3*x^4*2y + 3*x^2*4y^2 + 8y^3
= x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.
