Expression Simplification Techniques Quiz Quiz

Sharpen your math skills with this quiz focusing on key expression simplification techniques, including combining like terms, factoring, distributive property, and recognizing equivalent expressions. Enhance your proficiency in simplifying algebraic expressions efficiently and accurately.

1. Combining Like Terms

   Which of the following is the correct simplification of the expression 4x + 3y - 2x + 5y?

   1. 2x + 2y
   2. 6x + 2y
   3. 2x + 8y
   4. 4x + 8y

   Explanation: The expression combines like terms: 4x minus 2x gives 2x, and 3y plus 5y gives 8y, resulting in 2x + 8y. The option 6x + 2y incorrectly adds terms across variables. The option 4x + 8y fails to subtract 2x from 4x. The option 2x + 2y incorrectly adds the y terms. Only 2x + 8y correctly groups and simplifies both variables.

2. Distributive Property Application

   Using the distributive property, how is the expression 3(a + 4) − 2(a + 4) best simplified?

   1. a + 8
   2. a + 4
   3. 5a + 20
   4. a − 8

   Explanation: Applying distributive property: 3(a + 4) becomes 3a + 12, and 2(a + 4) becomes 2a + 8, giving 3a + 12 − 2a − 8. Simplifying yields (3a − 2a) + (12 − 8) = a + 4. The option 5a + 20 multiplies instead of subtracting. a − 8 is incorrect with signs and incorrect combining. a + 8 only adds, disregarding the subtraction.

3. Factoring Common Factors

   Which expression is equivalent to 12m − 18n after factoring out the greatest common factor?

   1. 3(4m − 6n)
   2. 12(m − 18n)
   3. 2(6m − 9n)
   4. 6(2m − 3n)

   Explanation: The greatest common factor of 12m and 18n is 6; factoring 6 from each term results in 6(2m − 3n). The other choices factor out smaller values or use incorrect expressions: 2(6m − 9n) and 3(4m − 6n) both factor out less than the greatest common factor. 12(m − 18n) incorrectly factors out 12 and changes the terms inside the parentheses to a format that isn't equivalent to the original.

4. Recognizing Equivalent Expressions

   Which expression below is mathematically equivalent to 2(x − 5) + 7x?

   1. 9x + 10
   2. 2x − 5 + 7x
   3. 9x − 10
   4. 2x + 12x − 5

   Explanation: Expanding 2(x − 5) gives 2x − 10, which when added to 7x yields 9x − 10. The option 9x + 10 has the wrong sign for the constant. Writing 2x − 5 + 7x leaves the expression unsimplified. The option 2x + 12x − 5 incorrectly multiplies 2 by 6 instead of distributing into (x − 5).

5. Simplifying Expressions with Exponents

   How can you simplify the expression y^3 × 2y^2 − y^3 × y^2?

   1. y^5 × 2 − y^6
   2. y^5
   3. y^5
   4. y^5

   Explanation: Multiplying y^3 by 2y^2 gives 2y^5, and y^3 × y^2 equals y^5, so the expression simplifies to 2y^5 − y^5, which equals y^5. The other options either unnecessarily complicate the structure or repeat the correct answer in a different form. Only y^5 accurately represents the final simplified form, while options with different exponents or unnecessary factors are incorrect.