# Polynomials

## Exercise 2.5 Part 4

Question 4: Expand each of the following using suitable identities:

(i) (x + 2y + 4z)^2

Answer: Given, (x + 2y + z)^2

Let, a = x, b = 2y and c = 4z

We know that, (a + b + c)^2

= a^2 + b^2 + c^2 + 2ab + 2bc + 2ac

So, the given expression can be written as follows:

x^2 + 4y^2 + 16z^2 + 4xy + 16yz + 8xz

(ii) (2x – y + z)^2

Answer: Given, (2y – y + z)^2

= [2x + (-y) +z]^2

= Let, a = 2x, b = - y and c = z

Using the identity (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc +2ac, we get;

(2x)^2 + (-y)^2 + z^2 + 2(2x(-y) + 2(-y)z + 2(2xz)

= 4x^2 + y^2 + z^2 + 2(-2xy) + 2(-yz) + 4xz
= 4x2 + y2 + z2 - 4xy – 2yz + 4xz

(iii) ( -2x + 3y + 2z)^2

Answer: Given, (- 2x + 3y + 2z)^2
Let, a= - 2x, b = 3y and c = 2z

Using the identity (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac, we get;

(-2x)^2 + (3y)^2 + (2z)^2 + 2( - 2x\xx3y) + 2(3y\xx2z) + 2(-2x\xx2z)

= 4x^2 + 9y^2 + 4z^2 + 2( - 6xy) + 2(6yz) + 2(-4xz)

= 4x^2 + 9y^2 + 4z^2 – 12xy + 12yz – 8xz`