Bicol Regional Science High School

Tuburan, Ligao City

WORKSHEET FACTORING
IN BY
MATHEMATICS 8 GCF

(1st GRADING)
Factor the following completely. Factor the following completely.

1. 18m - 24m3 + 9m2 1. 16y6-4y4+24y3-28

2. 125w – 25p3 2. -9a3b2c2-12a5b3c6+3a3b2c3-6a6b6c2

3. 7w6p9 + 54w8p2 – 121wp3 3. 2d3e3-8d5e2+4d3e2_12d7e4

9 5 4
4. 121d k – 22d m – 110d h 3 12 4. 12c3-15c2+21c

5. 216k 12n 11n 7n

g r + 27k g r 7n 8n 15n 5. 15x2+20xy+25x

6. 7j3o2 + 91o4t + 67o27z8 6. 36+81x

7. 81s10 – 36s11 7. 4a3b4-12ab3+16ab4

8. 48y 44m
– 64c32h
+ 80u 21a 8. 3c4+7c3-c2
20 5 14
9. 64b v + 32b v – 288b v 10 2 9. 4m5(m+n)+8m3(m+n)
45
10. 44f + 66f 40 10. 21x3(x+y)2-28x2(x+y)-35xb(x+y)4
 1. 9v2 – 25h4

2. 48f2n2 –12f8d4

3. 0.036c – 0.016c5
FACTORING 4. 9 – 954u2

5. h3– 64h
THE
6. t4 – 144b2
DIFFERENCE OF TWO 7. 3x2 – 75j8

8. 144z2 – 169a6
SQUARES
9. r8 – 81

10. s4 – 16

Factor the following completely.

Factor the following completely.

1. 121u6-49

2. 18w3x2-162wy2

3. 25v2x-9v2x
FACTORING
4. 144m2-16

5. 5r3s2-605rt2 THE
6. 16x4-(x+y)4
SUM & DIFFERENCE
7. a2/196-b2/169

8. 9x4-1 OF TWO
9. 12j4k2-27j2l2 CUBES
10. 1.44c4-2.25d2
Factor the following completely. Factor the following completely.

1. m6 + 216 1. x3 + 125

2. p3 – 343 2. a3 + 64

3. 64 – 729g3 3. 250x4 + 128x

4. 375t6z6 – 81f6v6 4. w3 − 64

5. 512a4 + 27a 5. 1029yx3 + 24y4

6. 343 – 729c6 6. x3 + 1

7. 8b4 + 216b 7. y3 + 27

8. 125v – v4 8. m3 + 8n3

9. 8x3 + 3 9. a3 + 343b3

10. i3 + u3 10. 343m3 + 64n3

\
 Factor the following completely.

1. 121e6o2 – 220e3opq3 + 100 p2q6

2. 49n2 – 126nm + 81m2

3. 0.36z4 – 0.60wz + 0.25w4

4. 27 – 18x + 3x2
FACTORING 6
5. 100y + 140x y + 49x2n n 3

PERFECT SQUARE TRINO- 6. 2h + 2h + 1

4 2

2 3 4
7. 200u – 80u + 8u
MIAL 8. 36k – 84k + 492

9. 80 p6 + 200p3 + 125

10. d2 – dj2 + j4
Factor the following completely.

1. d2 + 2bd + b2

2. bc2 + 2abc + a2 b

3. m2— 18m + 81

4. x2 + 8x + 16
2—
FACTORING
5. y 16y + 64

6. 16x 2 + 40x + 25 BY
7. 36v 2 − 132v + 121
GROUPING
8. 121m 2 − 198m + 81

9. 49 p 2 − 28p + 4

10. 100b 2 − 180b + 81

Factor the following completely. Factor the following completely.

1. xy + 2y + 3x + 6 1. 14mp3 + qp3— 14mp2 –qp2– 14mp— qp

2. 4x3 + 2x2-2x-1 2. 45ay— 9bx— 81by + 5ax

3. 2x2 + ay –ax2- 2y 3. x2 +6x + 9— 16y2

4. 24x3 - 6x2 + 8x - 2 4. 25wxy+ 35wv2 + 15uxy + 21uv2

5. 9x3 + 362 - 4x - 16 5. 4x2—64y2 + 80y—25

6. 14mp3 + ap - 14mp2 - ap2 - 14mp - ap 6. 7c + 7d +ct + dt

7. 45ay - 9bx - 81by + 5ax 7. h3+ 8f3 + 24f2g + 24 fg2 + 8g3

8. x2 + 6x + 9 - 16y2 8. 6mn + 9n + 4m + 6

9. 25wxy + 35wx2 + 15uxy + 21uy2 9. 70s2 + 49ms— 100ms— 70m2

10. 4x2 - 64y2 + 80y - 25 10. g2— 4y2 + 12xy– 9x2

 1. Two squares have a total area of 640 dm2. The larger square
has a side that measures a thrice the measure of a side of a
smaller square. What are the measures of the sides of the two
squares?

2. The numerical value of twice the volume of a

Cube is equal to the numerical value of 8 times the perimeter
of one of its face. What is the numerical value of the measure
WORD of a side of the cube?

3. The width of a rectangular garden is given by the expres-

PROBLEMS sion , x + 1. If the area is given by 6x2 + 4x— 2, what is the
length of the garden?

4. A square has an area of 81s2 — 38sq + 100q2 .

A.) What is the value of one side?
B.) What is the perimeter of the square?

5. The volume of a rectangular prism is 27p3 + 81p2 + 54p.

What are the possible value of each of the dimension of the
prism?
 FACTORING BY GCF
1. 3m (6 – 8m2 + 3m)
2. 25(5w – p3)
3. wp2 (7w5p8 + 54w7 – 121p)
4. 11d3(11d6k5 – 2dm – 10h12)
KEY TO 5. 27k7ng8nr7n (8k5ng3n + r8n)
6. o2 (7j3 + 91o2t + 67o25z8)
CORRECTIONS 7. 9s10 (9 – 4s)
8. 16 (3y44a – 4c32a + 5 u21a)
9. 32b10v (2b10v4 + b4 – 9v)
10. 22f40 (22f5 + 3)
1. 4y2(4y4-y2+6y-7) DIFFERENCE OF TWO SQUARES
2 3 2 5 2
2. 3a bc(-3abc-4a b c +abc -2a b c) 4 5 1. (3v – 5h2) (3v + 5h2)
2 2 3
3. 2d e(de -4d e+2de-6d e ) 5 3 2. 12f2 (2n – f3d2) (2n + f3d2)
2
4. 3c(4c -5c+7) 3. 0.4c (0.3 – 0.2c2) (0.3 – 0.2c2)

5. 5x(3x+4y+5) 4. 9 (1 – 4u) (1 + 4u)

6. 9(4+9x) 5. h (h – 8) (h + 8)
6. (t2 – 12b) (t2 + 12b)
7. 4ab3(a2b-3+4b)
7. 3 (x – 5j4) (x + 5j4)
8. c(3c3+7c2-c)
8. (12z – 13a3) (12z + 13a3)
9. 4m3(m+n))(m2+2)
9. (r4+9) (r2 + 3) (r2 – 3)
10. 7x(x+y) [3x2(x+y)-4x-5b(x+y)3]
10. (s2 + 4) (s + 2) (s – 2)
1. (11u3+7)(11u3-7) SUM AND DIFFERENCE OF TWO CUBES
2 2_ 2
2. 18w(w x 9y ) or 18w(wx+3y)(wx-3y) 1. (m2 + 6) (m4 – 6m2 + 36)
2 2
3. x(25v -9y ) or x(5v+3y)(5v-3y) 2. (p – 7) (p2 + 7p + 49)

4. (12m+4)(12m-4) 3. (4 – 9g) (16 + 36g + 49)

5. 5r(r2s2-121t2) or 5r(rs+11t)(rs-1t) 4. 3 (5t2z2 – 3f2v2) (25t4z4 + 15f2t2v2z2 + 9f4v4)

2 2
6. (4x +(x+y) )(4x -(x+y) ) 2 2 5. 9 (8a + 3) (64a2 – 24a + 9)
6. (7 – 9c2) (49 + 63c2 + 81c4)
7. (a/14+b/13)(a/14-b/13)
2
8. (3x +1)(3x -1) 2 7. 8b (b + 3) (b2 – 3b + 9)
2 2 2 2 2 2 2
9. 3j (4j k -9l ) or 3j (2j k +3l)(2j k -3l) 2 2 8. v (5 – v) (25 + 5v + v2)

10. (1.2c2+1.5d)(1.2c2-1.5d) 9. (2x + 1) (4x2 – 2x + 1)

10. (i + u) (i2 – iu + u2)
1. (x + 5) (x2 – 5x + 25) FACTORING PERFECT SQUARE TRINOMIALS
2
2. (a + 4) (a - 4a + 16) 1. (11e3o – 10pq3)2
2
3. 2x (5x + 4) (25 x —20x + 16) 2. (7n – 9m)2
2
4. ( w – 4) (w + 4w + 16 ) 3. (0.6z2 – 0.5w2)2
2
5. 3y (7x + 2y) (49x – 14xy + 4y )2 4. 3(3x + 1)2
5. (10 y3 + 7xn)2
6. (x + 1) (x2 - x + 1)
6. (h2 + 1)2
7. (y + 3) (y2 – 3y + 9)
7. 8u2 (5u – 1)2
8. (m + 2n) (m2— 2mn + 4n2)
8. (6k – 7)2
9. (2x + 1) (a – 7ab + 49b2)
9. 5(4p3 + 5)2
10. (i + u) (i2 – iu + u2)
10. d – j2)
 FACTORING BY GROUPING
1. (d+b)2
1. (x+2) (y+3)
2
2. (b + d)
2. (2x + 1) (2x2– 1)
3. (m— 9) 2
3. (x2-y) (2-a)
4. (x+4)2
4. 2 (3x2+1) (4x-1)
5. ( y – 8 )2
2
5. (x+4) (3x-2) (3x+2)
6. (4x + 5)
6. p[(14m+q) (p2-p-1)
7. (9y + x) (5a-9b)
2
7. (9y + x) (5a-9b)
8. ( 11m— 9)
2
8. [(x+3)+4y][(x+3)-4y]
9. ( 7p—2 )
9. (5xy+7v2)(5w + 3u)
10. (10b –9)2
10. [2x+(8y-5)][2x-(8y-5)]
 WORD PROBLEMS
1. p [(14m + q) ( p2—p—1 )]
1. 8dm
2. (9x + x) (5a – 9b) 2.
-8dm

3. [ (x + 3) + 4y ] [ (x + 3) - 4y] 2. 4 and –4

4. (5xy + 7v2) (5w + 3u) 3. 6x— 2

5. [ 2x + (8y—5)] [ 2x— (8y— 5)] 4. A.) 9s—10q

B.) 36s— 40q
6. (c + d) ( 7 + t )

7. [ h + (2f + 2g) ] [ h2—h (2f +2g) + (2f +2g )2 ] 5. 9p

(p + 1)
8. (2m + 3) (3n + 2)
(3p + 6)
9. (10s + 7m ) ( 7s— 10m)

10. [g + (2y– 3x) ] [ g— (2y— 3x) ]