Question

Find the polynomial. (2y − 9)(2y − 9) is the factored form of the expression .

Answer 1

(2y-9)(2y-9)
(2y-9)^2
(2y)^2-2*2y*9+9^2
4y^2-36y+81

Answer 2

Answer:

The polynomial whose factored form is  $(2y-9)(2y- 9)$

is  $4y^2+81-36y$

Step-by-step explanation:

Given : Factored form of a polynomial as $(2y-9)(2y- 9)$

We have to find the polynomial whose factored form is  $(2y-9)(2y- 9)$

Consider the given expression  $(2y-9)(2y- 9)$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

We have,

$\left(2y-9\right)\left(2y-9\right)=\:\left(2y-9\right)^{1+1}=\:\left(2y-9\right)^2$

Thus, Applying algebraic identity, $(a-b)^2=a^2+b^2-2ab$,  we have,

a = 2y and b = 9

Thus,  $(2y-9)^2=(2y)^2+9^2-2\cdot 2y \cdot 9$

Simplify, we have,

$(2y-9)^2=4y^2+81-36y$

Thus, The polynomial whose factored form is  $(2y-9)(2y- 9)$

is  $4y^2+81-36y$