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