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

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

is
`4y^2+81-36y`

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`