Question

Factor completely and then place the factors in the proper location on the grid. 8y 2 + 6y + 1

Answer 1

Factored form the given quadratic equation
`8y^2+6y+1` is
`(2y+1)(4y+1)`

Explanation:

Given :
`8y^2+6y+1`

We have to factorize the given equation completely and place the factors in the proper location on the grid.

Consider the given quadratic equation
`8y^2+6y+1`.

We solve the given quadratic equation using middle term splitting method,

6y can be written as 4y + 2y , then equation becomes,

`8y^2+6y+1=8y^2+4y+2y+1`

Taking 4y common from first two term and 1 common from last two term , we have,

`\Rightarrow 4y(2y+1)+1(2y+1)`

`\Rightarrow (2y+1)(4y+1)`

Thus, factored form the given quadratic equation
`8y^2+6y+1` is
`(2y+1)(4y+1)`

The placement of the factors in the proper location on the grid is shown in figure attached below.