Answer:
Option (c) is correct
The factors of the given equation \(4x^2+20x+25\) are \(=\left(2x+5\right)(2x+5)\)
Step-by-step explanation:
Given equation \(4x^2+20x+25\)
We have to find the factors of given equation and chosoe the correct option.
Consider the given equation \(4x^2+20x+25\)
Rewrite 4 as 2²
and 25 as 5²
We have,
\(=2^2x^2+20x+5^2\)
Apply exponent rule, \(a^mb^m=\left(ab\right)^m\)
we have,
\(=\left(2x\right)^2+20x+5^2\)
rewrite 20 x as \(\mathrm{\:as\:}2\cdot \:2x\cdot \:5\)
we have,
\(=\left(2x\right)^2+2\cdot \:2x\cdot \:5+5^2\)
Apply algebraic identity \(\left(a+b\right)^2=a^2+2ab+b^2\)
We have,
\(=\left(2x+5\right)^2\)
Thus, The factors of the given equation \(4x^2+20x+25\) are \(=\left(2x+5\right)(2x+5)\)
