Question

What is the quotient when x^4 + 4x^3y + 6x^2y + 4xy^3 + y^4 is divided by (x + y)?

(a) (x + y)^3

(b) x^2 + y^2

(c) (x + y)^2

(d) (x + y)

The question was asked by my school principal while I was bunking the class.

I would like to ask this question from Binomial Theorem for Positive Integral Index topic in chapter Binomial Theorem of Mathematics – Class 11

Answer 1

Right choice is (a) (x + y)^3

Easiest explanation: Using binomial expansions properties, x^4 + 4x^3y + 6x^2y + 4xy^3 + y^4 can be written as

= 4C0x^4y^0 + 4C1x^3y^1 + 4C2x^2y^2 + 4C3x^1y^2 + 4C4x^0y^4

= (x + y)^4

When divided by (x + y), we get (x + y)^3.