Worksheet titled "Multiplying Algebraic Terms 2" featuring various algebraic multiplication exercises.

It looks like you've uploaded an image containing a math worksheet titled "Q1 Multiplying Algebraic Terms 2", with several algebraic multiplication problems. Let's go through each problem step by step and solve them.

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Objective:

Multiply the given algebraic terms by combining coefficients (numbers) and variables (letters), using the rules of algebra:
- Multiply the numerical coefficients.
- Combine like variables by adding their exponents (e.g., $ x \times x = x^2 $).
- Keep unlike variables as separate terms.

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Let’s solve each part:

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#### a) $ 4x \times 3 $
- $ 4 \times 3 = 12 $
- $ x $ remains
- Answer: $ 12x $

#### b) $ 6x \times 5r $
- $ 6 \times 5 = 30 $
- $ x \times r = xr $
- Answer: $ 30xr $

#### c) $ 7gy \times 3 $
- $ 7 \times 3 = 21 $
- $ gy $ remains
- Answer: $ 21gy $

#### d) $ 9m \times 4d $
- $ 9 \times 4 = 36 $
- $ m \times d = md $
- Answer: $ 36md $

#### e) $ 13m \times 12n $
- $ 13 \times 12 = 156 $
- $ m \times n = mn $
- Answer: $ 156mn $

#### f) $ 2 \times 8w \times 3x $
- First, multiply numbers: $ 2 \times 8 \times 3 = 48 $
- Variables: $ w \times x = wx $
- Answer: $ 48wx $

#### g) $ 11q \times 4x \times 3 $
- Numbers: $ 11 \times 4 \times 3 = 132 $
- Variables: $ q \times x = qx $
- Answer: $ 132qx $

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Now continue with the second column:

#### h) $ 3e \times 5 $
- $ 3 \times 5 = 15 $
- $ e $ remains
- Answer: $ 15e $

#### i) $ 5t \times 7 $
- $ 5 \times 7 = 35 $
- $ t $ remains
- Answer: $ 35t $

#### j) $ 2 \times 11ht $
- $ 2 \times 11 = 22 $
- $ ht $ remains
- Answer: $ 22ht $

#### k) $ 3c \times 5b $
- $ 3 \times 5 = 15 $
- $ c \times b = bc $
- Answer: $ 15bc $

#### l) $ 6a \times 12d $
- $ 6 \times 12 = 72 $
- $ a \times d = ad $
- Answer: $ 72ad $

#### m) $ 11ab \times 3d \times 7 $
- Numbers: $ 11 \times 3 \times 7 = 231 $
- Variables: $ ab \times d = abd $
- Answer: $ 231abd $

#### n) $ 4a \times 3b \times 2c $
- Numbers: $ 4 \times 3 \times 2 = 24 $
- Variables: $ a \times b \times c = abc $
- Answer: $ 24abc $

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Now the third column:

#### o) $ 4d \times 6 $
- $ 4 \times 6 = 24 $
- $ d $ remains
- Answer: $ 24d $

#### p) $ 4x \times 3u $
- $ 4 \times 3 = 12 $
- $ x \times u = xu $
- Answer: $ 12xu $

#### q) $ 4x \times 6p $
- $ 4 \times 6 = 24 $
- $ x \times p = xp $
- Answer: $ 24xp $

#### r) $ 9g \times 2t $
- $ 9 \times 2 = 18 $
- $ g \times t = gt $
- Answer: $ 18gt $

#### s) $ 2ah \times 3c $
- $ 2 \times 3 = 6 $
- $ a \times h \times c = a h c $
- Answer: $ 6ahc $

#### t) $ 16xy \times 1.5 $
- $ 16 \times 1.5 = 24 $
- $ xy $ remains
- Answer: $ 24xy $

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Now the fourth column:

#### u) $ 3c \times 5 $
- $ 3 \times 5 = 15 $
- $ c $ remains
- Answer: $ 15c $

#### v) $ 7 \times 6p $
- $ 7 \times 6 = 42 $
- $ p $ remains
- Answer: $ 42p $

#### w) $ 10a \times 7h $
- $ 10 \times 7 = 70 $
- $ a \times h = ah $
- Answer: $ 70ah $

#### x) $ 2.5t \times 5b $
- $ 2.5 \times 5 = 12.5 $
- $ t \times b = tb $
- Answer: $ 12.5tb $

#### y) $ 4f \times 3gh $
- $ 4 \times 3 = 12 $
- $ f \times gh = fgh $
- Answer: $ 12fgh $

#### z) $ 3.5x \times 3y $
- $ 3.5 \times 3 = 10.5 $
- $ x \times y = xy $
- Answer: $ 10.5xy $

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✔ Final Answers Summary:

| Letter | Problem | Answer |
|--------|--------|--------|
| a | $ 4x \times 3 $ | $ 12x $ |
| b | $ 6x \times 5r $ | $ 30xr $ |
| c | $ 7gy \times 3 $ | $ 21gy $ |
| d | $ 9m \times 4d $ | $ 36md $ |
| e | $ 13m \times 12n $ | $ 156mn $ |
| f | $ 2 \times 8w \times 3x $ | $ 48wx $ |
| g | $ 11q \times 4x \times 3 $ | $ 132qx $ |
| h | $ 3e \times 5 $ | $ 15e $ |
| i | $ 5t \times 7 $ | $ 35t $ |
| j | $ 2 \times 11ht $ | $ 22ht $ |
| k | $ 3c \times 5b $ | $ 15bc $ |
| l | $ 6a \times 12d $ | $ 72ad $ |
| m | $ 11ab \times 3d \times 7 $ | $ 231abd $ |
| n | $ 4a \times 3b \times 2c $ | $ 24abc $ |
| o | $ 4d \times 6 $ | $ 24d $ |
| p | $ 4x \times 3u $ | $ 12xu $ |
| q | $ 4x \times 6p $ | $ 24xp $ |
| r | $ 9g \times 2t $ | $ 18gt $ |
| s | $ 2ah \times 3c $ | $ 6ahc $ |
| t | $ 16xy \times 1.5 $ | $ 24xy $ |
| u | $ 3c \times 5 $ | $ 15c $ |
| v | $ 7 \times 6p $ | $ 42p $ |
| w | $ 10a \times 7h $ | $ 70ah $ |
| x | $ 2.5t \times 5b $ | $ 12.5tb $ |
| y | $ 4f \times 3gh $ | $ 12fgh $ |
| z | $ 3.5x \times 3y $ | $ 10.5xy $ |

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🔍 Explanation of Key Concepts:

- Multiplying coefficients: Just multiply the numbers together.
- Variables: When multiplying variables, write them in alphabetical order (optional but standard), and combine like bases by adding exponents (though here most are single powers).
- Order doesn't matter due to commutative property: $ ab = ba $.
- Decimal numbers are treated just like whole numbers.

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