Question

Determine the coefficient of x 9y 3 in the expansion of (a) (x + y) 12, (b) (x + 2y) 12 , and (c) (2x − 3y) 12

Answer 1

Question :- Determine the coefficient of x and y in the expansion of (a) (x + y) 12, (b) (x + 2y) 12 , and (c) (2x − 3y) 12 ?

Solution :-

Coefficient :- A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

a) (x + y)12

→ 12(x + y)

→ 12x + 12y

So,

• coefficient of x = 12.
• coefficient of y = 12.

b) (x + 2y)12

→ 12(x + 2y)

→ 12x + 24y

So,

• coefficient of x = 12.
• coefficient of y = 24.

c) (2x - 3y)12

→ 12(2x - 3y)

→ 24x - 36y

So,

• coefficient of x = 24.
• coefficient of y = -36.