Question

factor.

1. $y^{2}-5y$
2. $4a^{2}+2a$
3. $6y^{2}+3y$
4. $y^{3}+9y^{2}$
5. $x^{3}+8x^{2}$
6. $3y^{2}-3y-9$
7. $5x^{2}-5x+15$
8. $6x^{2}-3x^{4}$
9. $8y^{2}+4y^{4}$
10. $4ab-6ac+12ad$
11. $8xy+10xz-14xw$
12. $4x^{2}y-12xy^{2}$
13. $5x^{2}y^{3}+15x^{3}y^{2}$
14. $x^{6}+x^{5}-x^{4}+x^{3}$
15. $y^{4}-y^{3}+y^{2}+y$
16. $24x^{3}-36x^{2}+72x$
17. $10a^{4}+15a^{2}-25a$
18. $y^{2}-6y+9$
19. $x^{2}-8x+16$
20. $x^{2}+14x+49$
21. $x^{2}+16x+64$
22. $x^{2}+1+2x$
23. $x^{2}+1-2x$
24. $a^{2}+4a+4$
25. $a^{2}-4a+4$
26. $y^{2}+36-12y$
27. $y^{2}+36+12y$
28. $-18y^{2}+y^{3}+81y$
29. $24a^{2}+a^{3}+144a$
30. $12a^{2}+36a+27$
31. $20y^{2}+100y+125$
32. $2x^{2}-40x+200$
33. $32x^{2}+48x+18$
34. $1-8d+16d^{2}$
35. $64+25y^{2}-80y$

Explanation:

Step1: Factor out GCF (1)

$y^2 - 5y = y(y - 5)$

Step2: Factor out GCF (2)

$4a^2 + 2a = 2a(2a + 1)$

Step3: Factor out GCF (3)

$6y^2 + 3y = 3y(2y + 1)$

Step4: Factor out GCF (4)

$y^3 + 9y^2 = y^2(y + 9)$

Step5: Factor out GCF (5)

$x^3 + 8x^2 = x^2(x + 8)$

Step6: Factor out GCF (6)

$3y^2 - 3y - 9 = 3(y^2 - y - 3)$

Step7: Factor out GCF (7)

$5x^2 - 5x + 15 = 5(x^2 - x + 3)$

Step8: Factor out GCF (8)

$6x^2 - 3x^4 = 3x^2(2 - x^2)$

Step9: Factor out GCF (9)

$8y^2 + 4y^4 = 4y^2(2 + y^2)$

Step10: Factor out GCF (10)

$4ab - 6ac + 12ad = 2a(2b - 3c + 6d)$

Step11: Factor out GCF (11)

$8xy + 10xz - 14xw = 2x(4y + 5z - 7w)$

Step12: Factor out GCF (12)

$4x^2y - 12xy^2 = 4xy(x - 3y)$

Step13: Factor out GCF (13)

$5x^2y^3 + 15x^3y^2 = 5x^2y^2(y + 3x)$

Step14: Factor out GCF (14)

$x^6 + x^5 - x^3 + x^2 = x^2(x^4 + x^3 - x + 1)$

Step15: Factor out GCF (15)

$y^4 - y^3 + y^2 + y = y(y^3 - y^2 + y + 1)$

Step16: Factor out GCF (16)

$24x^3 - 36x^2 + 72x = 12x(2x^2 - 3x + 6)$

Step17: Factor out GCF (17)

$10a^4 + 15a^2 - 25a = 5a(2a^3 + 3a - 5)$

Step18: Factor perfect square (18)

$y^2 - 6y + 9 = (y - 3)^2$

Step19: Factor perfect square (19)

$x^2 - 8x + 16 = (x - 4)^2$

Step20: Factor perfect square (20)

$x^2 + 14x + 49 = (x + 7)^2$

Step21: Factor perfect square (21)

$x^2 + 16x + 64 = (x + 8)^2$

Step22: Rearrange & factor (22)

$x^2 + 2x + 1 = (x + 1)^2$

Step23: Rearrange & factor (23)

$x^2 - 2x + 1 = (x - 1)^2$

Step24: Factor perfect square (24)

$a^2 + 4a + 4 = (a + 2)^2$

Step25: Factor perfect square (25)

$a^2 - 4a + 4 = (a - 2)^2$

Step26: Rearrange & factor (26)

$y^2 - 12y + 36 = (y - 6)^2$

Step27: Rearrange & factor (27)

$y^2 + 12y + 36 = (y + 6)^2$

Step28: Factor out GCF (28)

$y^3 - 18y^2 + 81y = y(y^2 - 18y + 81) = y(y - 9)^2$

Step29: Rearrange & factor GCF (29)

$a^3 + 24a^2 + 144a = a(a^2 + 24a + 144) = a(a + 12)^2$

Step30: Factor out GCF + square (30)

$12a^2 + 36a + 27 = 3(4a^2 + 12a + 9) = 3(2a + 3)^2$

Step31: Factor out GCF + square (31)

$20y^2 + 100y + 125 = 5(4y^2 + 20y + 25) = 5(2y + 5)^2$

Step32: Factor out GCF + square (32)

$2x^2 - 40x + 200 = 2(x^2 - 20x + 100) = 2(x - 10)^2$

Step33: Factor out GCF + square (33)

$32x^2 + 48x + 18 = 2(16x^2 + 24x + 9) = 2(4x + 3)^2$

Step34: Rearrange & factor (34)

$16d^2 - 8d + 1 = (4d - 1)^2$

Step35: Rearrange & factor (35)

$25y^2 - 80y + 64 = (5y - 8)^2$

Answer:

1. $y(y - 5)$
2. $2a(2a + 1)$
3. $3y(2y + 1)$
4. $y^2(y + 9)$
5. $x^2(x + 8)$
6. $3(y^2 - y - 3)$
7. $5(x^2 - x + 3)$
8. $3x^2(2 - x^2)$
9. $4y^2(2 + y^2)$
10. $2a(2b - 3c + 6d)$
11. $2x(4y + 5z - 7w)$
12. $4xy(x - 3y)$
13. $5x^2y^2(y + 3x)$
14. $x^2(x^4 + x^3 - x + 1)$
15. $y(y^3 - y^2 + y + 1)$
16. $12x(2x^2 - 3x + 6)$
17. $5a(2a^3 + 3a - 5)$
18. $(y - 3)^2$
19. $(x - 4)^2$
20. $(x + 7)^2$
21. $(x + 8)^2$
22. $(x + 1)^2$
23. $(x - 1)^2$
24. $(a + 2)^2$
25. $(a - 2)^2$
26. $(y - 6)^2$
27. $(y + 6)^2$
28. $y(y - 9)^2$
29. $a(a + 12)^2$
30. $3(2a + 3)^2$
31. $5(2y + 5)^2$
32. $2(x - 10)^2$
33. $2(4x + 3)^2$
34. $(4d - 1)^2$
35. $(5y - 8)^2$