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 \(4y^2+81-36y\)
