Question

factoring / distributive property worksheet
factor the expressions
1 a. 108 + 64z\t1 b. 44 + 20t
2 a. 84 + 77\t2 b. 108 + 63a
3 a. 8 + 12n\t3 b. 77 + 42y
4 a. 90t + 40\t4 b. 65w + 25
5 a. 40 + 54n\t5 b. 121z + 88
6 a. 121s + 99\t6 b. 55g + 36
7 a. 45 + 70t\t7 b. 22x + 14

Explanation:

Step1: Factor 108 + 64z (1a)

Find GCD of 108 and 64. Factors of 108: 2×2×3×3×3; Factors of 64: 2×2×2×2×2×2. GCD is 4.
Rewrite: \( 4\times27 + 4\times16z = 4(27 + 16z) \)

Step2: Factor 44 + 20t (1b)

GCD of 44 and 20. Factors: 44=2×2×11, 20=2×2×5. GCD=4.
Rewrite: \( 4\times11 + 4\times5t = 4(11 + 5t) \)

Step3: Factor 84 + 77 (2a)

GCD of 84 and 77. Factors: 84=7×12, 77=7×11. GCD=7.
Rewrite: \( 7\times12 + 7\times11 = 7(12 + 11) = 7\times23 = 161 \) (or keep factored: \( 7(12 + 11) \))

Step4: Factor 108 + 63a (2b)

GCD of 108 and 63. Factors: 108=9×12, 63=9×7. GCD=9.
Rewrite: \( 9\times12 + 9\times7a = 9(12 + 7a) \)

Step5: Factor 8 + 12n (3a)

GCD of 8 and 12. Factors: 8=4×2, 12=4×3. GCD=4.
Rewrite: \( 4\times2 + 4\times3n = 4(2 + 3n) \)

Step6: Factor 77 + 42y (3b)

GCD of 77 and 42. Factors: 77=7×11, 42=7×6. GCD=7.
Rewrite: \( 7\times11 + 7\times6y = 7(11 + 6y) \)

Step7: Factor 90t + 40 (4a)

GCD of 90 and 40. Factors: 90=10×9, 40=10×4. GCD=10.
Rewrite: \( 10\times9t + 10\times4 = 10(9t + 4) \)

Step8: Factor 65w + 25 (4b)

GCD of 65 and 25. Factors: 65=5×13, 25=5×5. GCD=5.
Rewrite: \( 5\times13w + 5\times5 = 5(13w + 5) \)

Step9: Factor 48 + 54n (5a)

GCD of 48 and 54. Factors: 48=6×8, 54=6×9. GCD=6.
Rewrite: \( 6\times8 + 6\times9n = 6(8 + 9n) \)

Step10: Factor 121z + 88 (5b)

GCD of 121 and 88. Factors: 121=11×11, 88=11×8. GCD=11.
Rewrite: \( 11\times11z + 11\times8 = 11(11z + 8) \)

Step11: Factor 121s + 99 (6a)

GCD of 121 and 99. Factors: 121=11×11, 99=11×9. GCD=11.
Rewrite: \( 11\times11s + 11\times9 = 11(11s + 9) \)

Step12: Factor 55g + 35 (6b)

GCD of 55 and 35. Factors: 55=5×11, 35=5×7. GCD=5.
Rewrite: \( 5\times11g + 5\times7 = 5(11g + 7) \)

Step13: Factor 45 + 70t (7a)

GCD of 45 and 70. Factors: 45=5×9, 70=5×14. GCD=5.
Rewrite: \( 5\times9 + 5\times14t = 5(9 + 14t) \)

Step14: Factor 22x + 14 (7b)

GCD of 22 and 14. Factors: 22=2×11, 14=2×7. GCD=2.
Rewrite: \( 2\times11x + 2\times7 = 2(11x + 7) \)

Answer:

1a. \( \boldsymbol{4(27 + 16z)} \)
1b. \( \boldsymbol{4(11 + 5t)} \)
2a. \( \boldsymbol{7(12 + 11)} \) (or \( \boldsymbol{161} \))
2b. \( \boldsymbol{9(12 + 7a)} \)
3a. \( \boldsymbol{4(2 + 3n)} \)
3b. \( \boldsymbol{7(11 + 6y)} \)
4a. \( \boldsymbol{10(9t + 4)} \)
4b. \( \boldsymbol{5(13w + 5)} \)
5a. \( \boldsymbol{6(8 + 9n)} \)
5b. \( \boldsymbol{11(11z + 8)} \)
6a. \( \boldsymbol{11(11s + 9)} \)
6b. \( \boldsymbol{5(11g + 7)} \)
7a. \( \boldsymbol{5(9 + 14t)} \)
7b. \( \boldsymbol{2(11x + 7)} \)