Product Formulas — Practice Quiz

A Algebra cheat sheet for Product Formulas — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. Expand the expression: $(3x + 4)^2$.

   • $9x^2 + 12x + 16$
   • $9x^2 + 24x + 16$
   • $9x^2 + 16$
   • $3x^2 + 24x + 16$

   Answer: $9x^2 + 24x + 16$

2. What is the expansion of $(5y - 2)^2$?

   • $25y^2 - 10y + 4$
   • $25y^2 - 20y + 4$
   • $25y^2 + 20y + 4$
   • $25y^2 - 4$

   Answer: $25y^2 - 20y + 4$

3. Expand $(x + 3)^3$.

   • $x^3 + 9x^2 + 27x + 27$
   • $x^3 + 3x^2 + 9x + 27$
   • $x^3 + 6x^2 + 18x + 27$
   • $x^3 + 9x^2 + 9x + 27$

   Answer: $x^3 + 9x^2 + 27x + 27$

4. Which of the following is the correct expansion of $(2a - 1)^3$?

   • $8a^3 - 12a^2 + 6a - 1$
   • $8a^3 - 6a^2 + 3a - 1$
   • $8a^3 + 12a^2 + 6a - 1$
   • $8a^3 - 12a^2 - 6a - 1$

   Answer: $8a^3 - 12a^2 + 6a - 1$

5. Expand $(x + y + 2)^2$.

   • $x^2 + y^2 + 4 + 2xy + 4x + 4y$
   • $x^2 + y^2 + 2 + 2xy + 2x + 2y$
   • $x^2 + y^2 + 4 + 2xy + 2x + 2y$
   • $x^2 + y^2 + 4 + xy + 2x + 2y$

   Answer: $x^2 + y^2 + 4 + 2xy + 4x + 4y$

6. Complete the expansion: $(m + 6)^2 = m^2 + \text{__} + 36$.

   • $6m$
   • $12m$
   • $6$
   • $12$

   Answer: $12m$

7. Find the missing term in the expansion: $(p - 2)^3 = p^3 - 6p^2 + \text{__} - 8$.

   • $4p$
   • $12p$
   • $6p$
   • $8p$

   Answer: $12p$

8. Which expression is equivalent to $4x^2 - 20x + 25$?

   • $(2x + 5)^2$
   • $(2x - 5)^2$
   • $(4x - 5)^2$
   • $(2x - 25)^2$

   Answer: $(2x - 5)^2$

9. Expand $(x^2 + 2y)^2$.

   • $x^4 + 4xy + 4y^2$
   • $x^4 + 2x^2y + 4y^2$
   • $x^4 + 4x^2y + 4y^2$
   • $x^4 + 4y^2$

   Answer: $x^4 + 4x^2y + 4y^2$

10. Expand $(a - b + c)^2$.

    • $a^2 + b^2 + c^2 - 2ab + 2ac - 2bc$
    • $a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$
    • $a^2 - b^2 + c^2 - 2ab + 2ac - 2bc$
    • $a^2 + b^2 + c^2 - 2ab - 2ac + 2bc$

    Answer: $a^2 + b^2 + c^2 - 2ab + 2ac - 2bc$