Let's solve each expression by
multiplying and simplifying algebraic expressions. We'll follow the rules of algebra:
- Multiply coefficients (numbers).
- Combine like variables using exponent rules: $ x^a \times x^b = x^{a+b} $
- Variables are multiplied by adding their exponents.
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Left Column
1.
$ 5x \times 2x \times 3y $
- Coefficients: $ 5 \times 2 \times 3 = 30 $
- Variables: $ x \times x = x^2 $, and $ y $
- Result: $ 30x^2y $
2.
$ 2 \times 2 \times 3x \times 4 $
- Coefficients: $ 2 \times 2 \times 3 \times 4 = 48 $
- Variable: $ x $
- Result: $ 48x $
3.
$ 2a \times 3ab \times 2c $
- Coefficients: $ 2 \times 3 \times 2 = 12 $
- Variables: $ a \times a = a^2 $, $ b $, $ c $
- Result: $ 12a^2bc $
4.
$ 9 \times x^2 \times xy $
- Coefficient: $ 9 $
- Variables: $ x^2 \times x = x^3 $, $ y $
- Result: $ 9x^3y $
5.
$ 4xy \times 2x^2y \times 7 $
- Coefficients: $ 4 \times 2 \times 7 = 56 $
- Variables: $ x \times x^2 = x^3 $, $ y \times y = y^2 $
- Result: $ 56x^3y^2 $
6.
$ 9x \times 2xy \times 3x^2 $
- Coefficients: $ 9 \times 2 \times 3 = 54 $
- Variables: $ x \times x \times x^2 = x^4 $, $ y $
- Result: $ 54x^4y $
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Right Column
1.
$ 2x \times 3y \times 2xy $
- Coefficients: $ 2 \times 3 \times 2 = 12 $
- Variables: $ x \times x = x^2 $, $ y \times y = y^2 $
- Result: $ 12x^2y^2 $
2.
$ 4 \times 2x \times 3x^2y $
- Coefficients: $ 4 \times 2 \times 3 = 24 $
- Variables: $ x \times x^2 = x^3 $, $ y $
- Result: $ 24x^3y $
3.
$ 10x \times 2y \times 3 $
- Coefficients: $ 10 \times 2 \times 3 = 60 $
- Variables: $ x $, $ y $
- Result: $ 60xy $
4.
$ 4xy^2 \times 2x^2y $
- Coefficients: $ 4 \times 2 = 8 $
- Variables: $ x \times x^2 = x^3 $, $ y^2 \times y = y^3 $
- Result: $ 8x^3y^3 $
5.
$ 9 \times xyz \times 4xy $
- Coefficients: $ 9 \times 4 = 36 $
- Variables: $ x \times x = x^2 $, $ y \times y = y^2 $, $ z $
- Result: $ 36x^2y^2z $
6.
$ 2x \times xy^2 \times 3xy $
- Coefficients: $ 2 \times 3 = 6 $
- Variables: $ x \times x \times x = x^3 $, $ y^2 \times y = y^3 $
- Result: $ 6x^3y^3 $
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✔ Final Simplified Answers:
#### Left Column:
1. $ 30x^2y $
2. $ 48x $
3. $ 12a^2bc $
4. $ 9x^3y $
5. $ 56x^3y^2 $
6. $ 54x^4y $
#### Right Column:
1. $ 12x^2y^2 $
2. $ 24x^3y $
3. $ 60xy $
4. $ 8x^3y^3 $
5. $ 36x^2y^2z $
6. $ 6x^3y^3 $
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Let me know if you'd like these arranged in a table or printed format!
Parent Tip: Review the logic above to help your child master the concept of simplify numerical expressions worksheet.
