Factoring Special Products Practice — Grade 9 math

Lesson 83: Factoring Special Products — Practice Questions

1. Factor the expression $x^2 - 81$ completely. The factored form is ___.
2. Which of the following binomials is considered prime and cannot be factored using the difference of two squares formula?
- A. $m^2 - 64$
- B. $m^2 + 64$
- C. $4m^2 - 9$
- D. $1 - m^2$
3. Use the difference of two squares formula to factor $9y^2 - 49$. The result is ___.
4. To factor $25x^2 - 1$ using the formula $a^2 - b^2 = (a+b)(a-b)$, what are the correct values for $a$ and $b$?
- A. $a = 5x, b = 1$
- B. $a = 25x, b = 1$
- C. $a = 5x^2, b = 1$
- D. $a = 12.5x, b = 0.5$
5. Completely factor the binomial $100 - p^2$. The factored expression is ___.
6. Factor the expression $p^2 - 81$. The factored form is ___.
7. Which of the following is the correct factored form of $16x^2 - 25$?
- A. (4x+5)(4x-5)
- B. $(4x-5)^2$
- C. (8x+5)(2x-5)
- D. (16x+5)(x-5)
8. Which of the following expressions represents a difference of two squares?
- A. $x^2 + 36$
- B. $x^2 - 18$
- C. $x^2 - 49$
- D. x - 49
9. Factor the expression $100a^6 - 9b^2$. The result is ___.
10. Which expression correctly factors the binomial $36m^2 - 121n^{10}$?
- A. $(6m + 11n^5)(6m - 11n^5)$
- B. $(6m - 11n^{10})^2$
- C. $(18m + 11n^5)(2m - 11n^5)$
- D. $(6m + 11n^{10})(6m - 11n^{10})$