Answer the following questions related to quadratic expressions:

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Answer the following questions related to quadratic expressions: (i) Prove that for any real number

k

, the polynomial

x^{2}+2kx+k^{2}

can be expressed as the square of a linear polynomial in

x

. (ii) Using the result of part (i), show that

4x^{2}+12xy+9y^{2}

can be expressed as the square of a binomial in

x

and

y

. (iii) Hence or otherwise, determine the value of

m

for which the polynomial

4x^{2}+12xy+9y^{2}-m

is exactly divisible by the binomial

x+\dfrac{3}{2}y