Question

Factoring by grouping

x^2 + 4y + 2x + 2xy
pls explain with work too!!!

Answer 1

`\tt \: {x}^(2) + 4y + 2x + 2xy`

Factor out x from the expression

`\tt \: x * (x + 2) + 4y + 2xy`

Factor out 2y from the expression

`\tt \: x * (x + 2) + 2y * (2 + x)`

Factor out x+2 from the expression

`\boxed{ \sf \: (x + 2) * (x + 2y)}`

➪ Therefore, The factors are: (x+2) & (x+2y)

Answer 2

`{x}^(2) + 4y + 2x + 2xy`

We can factorise this expression by grouping. First let us arrange it in this way

`= {x}^(2) + 2xy + 2x + 4y`

Let us bracket them like this:

`= ( {x}^(2) + 2xy) + (2x+ 4y)`

In the first bracket portion, take x as common and in the second expression, take 2 as common.

`= x(x + 2y) + 2(x + 2y) \\ = (x + 2)(x + 2y)`

Answer:

`(x + 2)(x + 2y)`

Hope you could understand.

If you have any query, feel free to ask.