Question

What do we get after expanding (p+3q-2z)^2?

(a) p^2 + 9q^2 + 4z^2 + 6pq – 12qz + 4zp

(b) p^2 + 9q^2 + 4z^2 + 12pq + 12qz + 4zp

(c) p^2 + 9q^2 + 4z^2 – 12pq – 12qz – 4zp

(d) p^2 + 9q^2 + 4z^2 + 6pq – 12qz – 4zp

The question was asked in an interview for internship.

This key question is from Factorisation of Polynomials and Algebraic Identities in chapter Polynomials of Mathematics – Class 9

Answer 1

Right option is (d) p^2 + 9q^2 + 4z^2 + 6pq – 12qz – 4zp

Explanation: We know that (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

(p+3q-2z)^2can also be written as (p+3q+(-2z))^2.

Here, a = p, b = 3q and c = -2z

Therefore, using that formula we get (p+3q+(-2z))^2

= p^2 + (3q)^2 + (-2z)^2 + 2(p)(3q) + 2(3q)(-2z) + 2(-2z)(p)

= p^2 + 9q^2 + 4z^2 + 6pq – 12qz – 4zp.