Question

The second term of (x – 2y)^4 is

Answer 1

Answer:

Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=

n

∑

k=0 nCk⋅(an-kbk).

4

∑

k=0

4!

(4-k)!k!

⋅(x)4-k⋅(2y)k

Expand the summation.

4!

(4-0)!0!

(x)4-0⋅(2y)0+

4!

(4-1)!1!

(x)4-1⋅(2y)+

4!

(4-2)!2!

(x)4-2⋅(2y)2+

4!

(4-3)!3!

(x)4-3⋅(2y)3+

4!

(4-4)!4!

(x)4-4⋅(2y)4

Simplify the exponents for each term of the expansion.

1⋅(x)4⋅(2y)0+4⋅(x)3⋅(2y)+6⋅(x)2⋅(2y)2+4⋅(x)⋅(2y)3+1⋅(x)0⋅(2y)4

Simplify each term.

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x4+8x3y+24x2y2+32xy3+16y4