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

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

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.