Question

Factor completely and then place the factors in the proper location on the grid. 4n 2 + 28n + 49

Answer 1

The equation is a perfect square binomial (2n+7)^2.

Answer 2

Answer:

The given  quadratic equation $4n^2+28n+49$ factored as $(2n+7)^2=(2n+7)(2n+7)$

Step-by-step explanation:

   Given quadratic equation $4n^2+28n+49$  

We have to factorize the given quadratic equation and make the grid of factors.

Consider the given quadratic equation $4n^2+28n+49$  

Using algebraic identity,

$(a+b)^2=a^2+2ab+b^2$

On comparing, we get,

$a^2=4n^2\\\\ \Rightarrow a=2n$

also, $b^2=49\\\\\Rightarrow b=7$

Thus, the given  quadratic equation $4n^2+28n+49$ factored as $(2n+7)^2=(2n+7)(2n+7)$

The grid is shown in attachment below.