Question

Find the expansion of (x+y)^4

a) Using combinatorial reasoning.
b) Using the binomial theorem.
c) Using calculus-based expansion.
d) None of the above.

Answer 1

The expansion of (x+y)^4 can be found using combinatorial reasoning, the binomial theorem, or calculus-based expansion. The correct answer is b) Using the binomial theorem.

Step-by-step explanation:

The expansion of (x+y)^4 using combinatorial reasoning can be found by considering the binomial coefficients. The expansion using combinatorial reasoning is:

(x+y)^4 = 1*x^4 + 4*x^3*y + 6*x^2*y^2 + 4*x*y^3 + 1*y^4

The expansion using the binomial theorem is:

(x+y)^4 = x^4 + 4*x^3*y + 6*x^2*y^2 + 4*x*y^3 + y^4

The expansion using calculus-based expansion is:

(x+y)^4 = x^4 + 4*x^3*y + 6*x^2*y^2 + 4*x*y^3 + y^4

Therefore, the correct answer is b) Using the binomial theorem.