Question

Guys......✋✋

Help the gurl out ^_^

✴Show me the method of..

✔ Adding variable with same or different powers..

✔ Multiplying variables with same or different powers

✔Subtracting variables with same or different powers

✔ Dividing variables with same or different powers

Thanks ♥

Answer 1

нι тнєяє!

нєяє'ѕ уσυя αиѕωєя:-

1. ᴍᴇᴛʜᴏᴅ ᴏꜰ ᴀᴅᴅɪɴɢ ᴏʀ ꜱᴜʙᴛʀᴀᴄᴛɪɴɢ ᴠᴀʀɪᴀʙʟᴇꜱ ᴡɪᴛʜ ꜱᴀᴍᴇ ᴏʀ ᴅɪꜰꜰᴇʀᴇɴᴛ ᴩᴏᴡᴇʀꜱ:

To add or subtract with same or different powers, both the variables and the exponents of the variables must be the same.
You need to perform the required operations on the coefficients, leaving the variable and exponent as they are.
When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers.

ᴇxᴀᴍᴩʟᴇ 1:
x + x + x = 3x

ʜᴇʀᴇ, ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇ ʜᴀꜱ ꜱᴀᴍᴇ ʙᴀꜱᴇ ᴀɴᴅ ꜱᴀᴍᴇ ᴩᴏᴡᴇʀ ɪ.ᴇ. 1. ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴀᴅᴅɪᴛɪᴏɴ ᴏʀ ꜱᴜʙᴛʀᴀᴄᴛɪᴏɴ - ʙᴏᴛʜ ᴀʀᴇ ᴩᴏꜱꜱɪʙʟᴇ.

ᴇxᴀᴍᴩʟᴇ 2:
2x + 3x^2 + 5x^3 - 2x^2 - 3x - 1
= 5x^3 + (3x^2 - 2x^2) + (2x - 3x) - 1
= 5x^3 + (3 - 2)x^2 + (2 - 3)x - 1
= 5x^3 + x^2 - x - 1

ꜱᴏᴍᴇᴛɪᴍᴇꜱ, ɴᴏᴛ ᴀʟʟ ᴏꜰ ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴀɴᴅ ᴩᴏᴡᴇʀꜱ ᴡɪʟʟ ʙᴇ ᴛʜᴇ ꜱᴀᴍᴇ — yᴏᴜ ᴍᴀy ᴇɴᴄᴏᴜɴᴛᴇʀ ᴀ ᴩʀᴏʙʟᴇᴍ ᴛʜᴀᴛ ʜᴀꜱ ꜱᴇᴠᴇʀᴀʟ ɢʀᴏᴜᴩꜱ ᴏꜰ ᴠᴀʀɪᴀʙʟᴇꜱ ᴀɴᴅ ᴩᴏᴡᴇʀꜱ ᴛʜᴀᴛ ᴀʀᴇ ɴᴏᴛ ᴛʜᴇ ꜱᴀᴍᴇ. ɪɴ ᴛʜɪꜱ ᴄᴀꜱᴇ, yᴏᴜ ᴏɴʟy ᴀᴅᴅ ᴏʀ ꜱᴜʙᴛʀᴀᴄᴛ ᴛᴇʀᴍꜱ ᴡʜᴏꜱᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴀɴᴅ ᴩᴏᴡᴇʀꜱ ᴀʀᴇ ᴛʜᴇ ꜱᴀᴍᴇ.
(Notice that the exponents are listed in order from highest to lowest. This is a common practice to make answers easy to compare.)

ᴇxᴀᴍᴩʟᴇ 3:
x^2 - 2x^2 + 3x^2 + 3x^2 = 5x^2

ʜᴇʀᴇ, ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴀʀᴇ ᴛʜᴇ ꜱᴀᴍᴇ (x) ᴀɴᴅ ᴛʜᴇ ᴩᴏᴡᴇʀꜱ ᴀʀᴇ ᴀʟꜱᴏ ᴛʜᴇ ꜱᴀᴍᴇ (2). ᴛʜᴜꜱ, ᴡᴇ ᴄᴀɴ ᴩᴇʀꜰᴏʀᴍ ᴛʜᴇ ʀᴇqᴜɪʀᴇᴅ ᴏᴩᴇʀᴀᴛɪᴏɴꜱ ᴏɴ ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇꜱ.

ᴇxᴀᴍᴩʟᴇ 4:
4x^4 - 3x^3 + 2x^2 + x + 1

ᴀʟᴛʜᴏᴜɢʜ ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇꜱ ᴀʀᴇ ᴛʜᴇ ꜱᴀᴍᴇ (x), ᴛʜᴇ ᴩᴏᴡᴇʀꜱ ᴀʀᴇɴ'ᴛ ᴛʜᴇ ꜱᴀᴍᴇ (1, 2, 3, and 4). ᴛʜᴜꜱ, ᴡᴇ ᴄᴀɴ’ᴛ ꜱɪᴍᴩʟɪꜰy ᴛʜᴇꜱᴇ ᴛᴇʀᴍꜱ ʙᴇᴄᴀᴜꜱᴇ ᴀʟᴏɴɢ ᴡɪᴛʜ ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇꜱ, ᴛʜᴇ ᴩᴏᴡᴇʀꜱ ᴀʟꜱᴏ ɴᴇᴇᴅ ᴛᴏ ʙᴇ ᴛʜᴇ ꜱᴀᴍᴇ.
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2. ᴍᴇᴛʜᴏᴅ ᴏꜰ ᴍᴜʟᴛɪᴩʟyɪɴɢ ᴠᴀʀɪᴀʙʟᴇꜱ ᴡɪᴛʜ ꜱᴀᴍᴇ ᴏʀ ᴅɪꜰꜰᴇʀᴇɴᴛ ᴩᴏᴡᴇʀꜱ:

When you multiply two numbers or variables with the same base, you simply add the exponents. This is true for both numbers and variables.

For example, 2^3*2^7= 2^10 and c^3*c^4 = c^7.

When you include other numbers or variables in the multiplication, you simply break it up into several multiplications, such as (x*10^5)*(x*10^3) = x^2*10^8.
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3. ᴍᴇᴛʜᴏᴅ ᴏꜰ ᴅɪᴠɪᴅɪɴɢ ᴠᴀʀɪᴀʙʟᴇꜱ ᴡɪᴛʜ ꜱᴀᴍᴇ ᴏʀ ᴅɪꜰꜰᴇʀᴇɴᴛ ᴩᴏᴡᴇʀꜱ:

We divide exponential expressions, leaving the answers as exponential expressions, as long as the bases are the same.
To divide exponents (or powers) with the same base, we subtract the exponents.
Division is the opposite of multiplication because we "add" the exponents when multiplying numbers with the same base whereas we "subtract" the exponents while dividing the numbers with the same base.

For example,
${2x}^{10} \div {2x}^{4} = {2x}^{10 - 4} = {2}^{6}$
Another Example:
$\frac{4 {x}^{6} {y}^{3} {z}^{2} }{2 {x}^{4} {y}^{3} z} = {2x}^{6 - 4} {y}^{3 - 3} {z}^{2 - 1} = {2x}^{2} {y}^{0} {z}^{1} = 2 \times {x}^{2} \times 1 \times z = 2 {x}^{2} z$
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нσρє ιт нєℓρѕ! :-)

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