Question

Expand Using the Binomial Theorem (x+2y)³

a) x³ + 6x²y + 12xy² + 8y³
b) x³ + 8x²y + 12xy² + 8y³
c) x³ + 6x²y + 8xy² + 8y³
d) x³ + 8x²y + 8xy² + 8y³

Answer 1

To expand (x+2y)³ using the Binomial Theorem, the simplified expression is x³ + 6x²y + 12xy² + 8y³.

Step-by-step explanation:

To expand (x+2y)³ using the Binomial Theorem, we use the formula:

(a+b)³ = a³ + 3a²b + 3ab² + b³

So, in this case, we have:

(x+2y)³ = x³ + 3x²(2y) + 3x(2y)² + (2y)³

Simplifying further, we get:

x³ + 6x²y + 12xy² + 8y³