Download Algebra 2: Exponents and Polynomials

Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E5: Factoring Special Products | VERSION B Factor the perfect square trinomials. 1.
𝑦 ! + 4𝑦 + 4 = Factor the following as the difference of two squares. Be sure to factor completely. 6.
𝑦 ! − 16 = 2.
𝑦 ! − 10𝑦 + 25 = 7.
49𝑎 ! − 25𝑏 ! = 3.
25𝑎 ! + 30𝑎 ! + 9 = 8.
640 − 10𝑡 ! = !
9.
𝑥 ! − 625 = 4.
5.
!
+
!
!
𝑡2 + 𝑡4 = 48𝑥 ! − 24𝑥 + 3 = 10. !
!"#
𝑥4 −
!
!"
= www.varsitylearning.com 1 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E5: Factoring Special Products | VERSION B Factor completely. 11. 𝑎 + 5
!
16. 𝑎 ! 𝑎 + 3 − 10𝑎 𝑎 + 3 + 25 𝑎 + 3 = − 9 = Factor the following as the sum or difference of two cubes. 12. 𝑎 ! − 2𝑎𝑦 + 𝑦 ! − 𝑥 ! = 13. 2𝑥 ! − 3𝑥 ! − 32𝑥 + 48 = 14. 2𝑥 + 3
!
− 16 = 15. 5𝑎 + 2
!
− 𝑥 ! = 17. 𝑥 ! + 8 = 18. 27 + 𝑎 ! = 19. 27𝑎 ! − 64𝑏 ! = 20. Find two values of 𝑏 that will make 49𝑥 ! + 𝑏𝑥 + 16 a perfect square trinomial. 𝑏 = www.varsitylearning.com 2 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E5: Factoring Special Products | VERSION B Factor the perfect square trinomials. 1.
𝑦 ! + 4𝑦 + 4 = (𝑦 + 2)! Factor the following as the difference of two squares. Be sure to factor completely. 6.
𝑦 ! − 16 = 𝑦 + 4 𝑦 − 4 2.
𝑦 ! − 10𝑦 + 25 = 𝑦 − 5 ! 7.
49𝑎 ! − 25𝑏 ! = 7𝑎 + 5𝑏 7𝑎 − 5𝑏 3.
25𝑎 ! + 30𝑎 ! + 9 = 5𝑎 ! + 3 ! 8.
640 − 10𝑡 ! = 10 8 + 𝑡 8 − 𝑡 9.
𝑥 ! − 625 = 𝑥 ! + 25 𝑥 + 5 𝑥 − 5 4.
5.
!
!
+
!
!
𝑡2 + 𝑡4 = 1
+ 𝑡!
3
!
48𝑥 ! − 24𝑥 + 3 = 3 4𝑥 − 1 ! 10. !
!"#
𝑥4 −
!
!"
= 1 ! 1
𝑥 +
25
4
1
1
𝑥+
5
2
1
1
𝑥 − 5
2
www.varsitylearning.com 3 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E5: Factoring Special Products | VERSION B Factor completely. 11. 𝑎 + 5
!
− 9 = 𝑎 + 2 𝑎 + 8 12. 𝑎 ! − 2𝑎𝑦 + 𝑦 ! − 𝑥 ! = 𝑎 − 𝑦 + 𝑥 𝑎 − 𝑦 − 𝑥 16. 𝑎 ! 𝑎 + 3 − 10𝑎 𝑎 + 3 + 25 𝑎 + 3 = 𝑎 − 5 ! 𝑎 + 3 Factor the following as the sum or difference of two cubes. 17. 𝑥 ! + 8 = 𝑥 + 2 𝑥 ! − 2𝑥 + 4 13. 2𝑥 ! − 3𝑥 ! − 32𝑥 + 48 = 2𝑥 − 3 𝑥 + 4 𝑥 − 4 18. 27 + 𝑎 ! = 3 + 𝑎 9 − 3𝑎 + 𝑎 ! 14. 2𝑥 + 3
!
15. 5𝑎 + 2
!
− 16 = 2𝑥 + 7 2𝑥 − 1 − 𝑥 ! = 5𝑎 + 2 + 𝑥 5𝑎 + 2 − 𝑥 19. 27𝑎 ! − 64𝑏 ! = 3𝑎 − 4𝑏 9𝑎 ! + 12𝑎𝑏 + 16𝑏 ! 20. Find two values of 𝑏 that will make 49𝑥 ! + 𝑏𝑥 + 16 a perfect square trinomial. 𝑏 = −56, 56 www.varsitylearning.com 4