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replace variable with number.
3g means 3 multiplies g
5(r) means 5 multiplies r

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3g = 3 times g

7hg (h = 3, g = 1) = 7 times 3 = 21 x 1= 21

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/ = divide
7g = 7 x g

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Like terms : Terms with the same variable.
Take note
6a and 8a² are unlike terms.
5xy and 10yx are like terms.
y is the same as 1y

Simplifying means making the expression shorter. This can be done by combining like terms.

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3 + 4x2 + 2x

3 = 3

4x² + 2x = Not Allowed (doesn't have power)

2x = 2x

Final Question:
3 + 4x2 + 2x

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34x + 2 + x =?

2 = 2

34x + x (invisible 1) = 35x

35x + 2 = ?

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Numbers are multiplied together.
Like terms are grouped together and can be simplified.
Example:
a3 x a2 = aaaaa = a5
It looks like exponents are added up.

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3xyz x 5xyz2 = 15x²y²z³

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12a⁵b³c¹t4 x 3 a⁶fdt = 36 a¹¹b³c¹t⁵df

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We use our prior knowledge on numbers here.
10/10 = 1
25/25 = 1
Since anything divide by the same number always gives us 1...
k/k = 1
When we have variables are the top and bottom of the fractions, we can cancel them out.

Example 1

Example

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35a2 ÷ 5a = 7a

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I chose this picture because it describes me perfectly, I can do it but i'm no master

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"Rainbow" method
3a(2-2b)
We do 3a x 2 =6a
and .    3a x -2b = -6ab
Must be careful with the signs.
The terms are unlike, so it cannot be further combined.
Final answer: 6a

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2(3a - 5)
1). Do the rainbow method to find out which numbers are multiplying which.
2). Do the math;
2 x 3a = 6a

2 x -5 = -10

3). Find the final question;
FINAL QUESTION
6a - 10

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3(2a - 6w) + 4(7w + 4a)

1). Do the math individually;

3(2a - 6w)  |  4(7w + 4a)

2). Do the rainbow method for the first set of brackets;

3). Do the math;
3 x 2a = 6a

3 x 6w = 18w

4).  Repeat for second set of brackets;
4 x 7w = 28w

4 x 4a = 16a

5). Rewrite the question (MAKE SURE TO ADD BACK THE ADDITION SIGN);
6a + 18w + 28w + 16a

6). Do stair case line;

7). Then add up the like terms'

6a + 16a = 22a

18w + 28w = 46w

8). Final Question;

22a + 46w =