Answer:
Factor of Equation [tex]4n^2+28n+49[/tex] is [tex]\left(2n+7\right)\left(2n+7\right)[/tex]
Step-by-step explanation:
Given : Equation [tex]4n^2+28n+49[/tex]
We have to factorize the given equation completely.
Consider the given equation [tex]4n^2+28n+49[/tex]
We can rewrite [tex]4n^2=2^2n^2[/tex] , we get,
[tex]=2^2n^2+28n+49[/tex]
We can rewrite [tex]49=7^2[/tex] , we get,
[tex]=2^2n^2+28n+7^2[/tex]
Apply exponent rule, [tex]a^mb^m=\left(ab\right)^m[/tex]
[tex]=\left(2n\right)^2+28n+7^2[/tex]
Apply identity, [tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex] ,we get,
[tex]\left(2n+7\right)^2[/tex]
Thus, Factor of Equation [tex]4n^2+28n+49[/tex] is [tex]\left(2n+7\right)\left(2n+7\right)[/tex]
