Question

divide the following method of factorisation
can anyone explain this ?​

Answer 1

ᴀɴsᴡᴇʀ:

${x}^{2} + 4xy + 4 {y}^{2} \div (x + 2y)$

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

$\: \: \: \: \: \: \: \: \: \: \: \: x + 2y$

____________________

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

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x {}^{2} + 2xy$

___________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2xy + 4xy {}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: 2xy + 4y {}^{2}$

_____________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0$

$= x + 2y$

ᴇxᴘʟᴀɪɴᴛɪᴏɴ :

1. ғʀɪsᴛ ᴡᴇ ᴅɪᴠɪᴅᴇᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ʙʏ sᴀᴍʟʟᴇsᴛ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ ᴡʜɪᴄʜ ᴅɪᴠɪᴅᴇ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴇxᴀᴄᴛʟʏ
2. ᴡᴇ ᴅɪᴠɪᴅᴇᴅ ᴛʜᴇ ǫᴜᴏᴛɪᴇɴᴛ ᴀɢᴀɪɴ ʙʏ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ ɪғ ɪᴛ ɪs ɴᴏᴛ ᴇxᴀᴄᴛʟʏ ᴅɪᴠɪᴅᴇᴅ ʙʏ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ
3. ᴡᴇ ᴍᴜʟɪᴛɪᴘʟᴇ ᴀʟʟ ᴛʜᴇ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ.

ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ᴏғ ғʀᴀᴄᴛᴏʀɪᴢᴀᴛɪᴏɴ ᴍᴇᴛʜᴏᴅ :

ᴛʜᴇ ɢᴇɴᴇʀᴀʟ ғʀᴀᴄᴛᴏʀɪᴢᴀᴛɪᴏɴ ғᴏʀᴍᴜʟᴀ ᴇxᴘʀᴇssᴇᴅ ᴀs

$n = {x}^{a} \times {y}^{b} \times {z}^{c}$

ʜᴇʀᴇ a,b,c ʀᴇᴘʀᴇsɴᴛ ᴛʜᴇ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ᴘᴏᴡᴇʀs ᴏғ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ᴏғ ғʀᴀᴄᴛᴏʀᴢɪᴇᴅ ɴᴜᴍʙᴇʀ

Answer 2

${x}^{2} + 4xy + 4 {y}^{2} \div (x + 2y)$

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

$\: \: \: \: \: \: \: \: \: \: \: \: x + 2y$

____________________________________

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

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x {}^{2} + 2xy$

___________________________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2xy + 4xy {}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: 2xy + 4y {}^{2}$

___________________________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0$

[tex] = x + 2y[/tex