LATIHAN 1.1

1. Jumlahkan bentuk–bentuk aljabar berikut:

a. 15x – 4 dan 4x + 7

= (15x–4) + (4x+7)

= 15x–4+4x+7

= 19x+3

b. 4x2 + 9x dan 3x – 5

= 4x2+9x+3x–5

= 4x2+12x–5

c. 5x2 – 4x + 10 dan 7x2 + 10x – 32

=(5x2 – 4x + 10)+(7x2 + 10x – 32)

= 5x2 – 4x + 10+7x2 + 10x – 32

=12x2+6x–22

d. 13a + 2b, –9a – 7b, dan 30a – 12b

= (13a + 2b)+(–9a – 7b)+(30a – 12b)

= 13a+2b–9a–7+30a–12b

= 34a–10b–7

e. y4 + 3y2 – y, y3 – 11y2 + 12y, dan y2 + 6y – 11

= (y4+3y2–y) + (y3–11y2+12y) + (y2+6y+11)

= y4+3y2–y+y3–11y2+12y+y2+6y+11

= y4+y3+9y2+17y+11

f. 8p – 2q, 13q – 7p + r, 11r – q, dan 6p – 8r= (8p – 2q)+(13q – 7p + r)+(11r – q)+(6p – 8r)

= 8p–2q+13q–7p+r+11r–q+6p–8r

= 7p+10q+4r

g. –2a + 3 dan 4a – 9

= (–2a+3) + (4a–9)

= –2a+3+4a–9

= 2a–6

h. 6xy + 5x – 12 dan –2xy + 7 – 3x

= 6xy + 5x – 12 –2xy + 7 – 3x = 4xy + 2x – 5

i. 8a + 2b, –3a + 5b, dan 24a – 11b

= 8a + 2b –3a + 5b + 24a – 11b

= 29a – 5b

j. 24p – 16q, 5q – 2r + 5, 11p – 2s, dan 9r + 3s

= 24p – 16q + 5q – 2r + 5 + 11p – 2s + 9r + 3s

= 35p – 11q + 7r + s + 5

= 24p – 16q, 5q – 2r + 5, 11p – 2s, dan 9r + 3s

2. Selesaikan bentuk–bentuk berikut:

a. (8x + 4y) – (3x – 2y)= 8x + 4y – 3x – 2y= 5x + 2y

b. (3x2 + 6x + 8) – (2x2 + 3x – 8) = 3x2 + 6x + 8 – 2x2 + 3x – 8= 6 + 6x + 8 – 4 + 3x – 8= 2 + 9x – 4

c. (–7a + 5b) – (10a + b) = –7a + 5b – 10a + b= –17a + 6b

d. (12p – 3q + 4r) – (6p + 7q – 2r) =12p – 3q + 4r – 6p + 7q – 2r= 6p + 4q +2r

e. (2x4 + x3 – 7x2) – (10x2 – 3x3 + x4)= 2x4 + x3 – 7x2 – 10x2 – 3x3 + x4

= –1 + x4 + x3 – 17x2

= 2x4 + x3 – 7x2 – 10x2 – 3x3 + x4

f. (17s + 5t – 2st) – (st + 2s – 4t)=17s + 5t – 2st – st + 2s – 4t=19s + t – 3st

g. (4 + 3m) – (8 – 2m)= 4 + 3m – 8 – 2m= –4 + m

h. (8y – 7z) – (2z + 9y)= 8y – 7z – 2z + 9y=17y – 9z

i. (3x2 + 5y – 7) – (2x2 + 12 – y)= 3x2 + 5y – 7 – 2x2 + 12 – y= 6 + 5y – 7 – 4 + 12 – y=7 + 4y

j. (3p – 8q + 9r) – (–12p + 2q – r)= 3p – 8q + 9r + 12p + 2q – r= 15p - 6q + 8r

3. Selesaikan bentuk–bentuk berikut:

a. 2x2 (3x – 4)= 6x3-8x2

b. (9p2q + 7q3) . (–9pq)= -81p3q2-63pq4

c. (12a – b) . (a + 2ab)=12a2 + 24a2b - ab – 2ab2

d. (–2 + 7a2) . (6b3 + c4)= -12 b3 + (-2c4) + 42a2b3 + 7a2c4

= -12 b3 - 2c4 + 42a2b3 + 7a2c4

e. (3x2 – 5x + y) . (–10x + 7y + 2y2)= - 30x2 + 21x2y + 6x2y2 + 50x2 - 35xy – 10xy2 – 10xy + 7y2 + 2y2

= 20x2 + 21x2y + 6x2y2 - 45xy – 10xy2 + 9y2

f. (3/2 x2y + 5yz + y) . (6y2 + 2yz + 9z3)

= 9x2y3 + 3x2y2z + 27/2x2 y z3 + 30y3z + 10y2z2 + 45yz4 + 6y3 + 2y2z + 9yz3

g. abc . (a + 2b)= a2bc + 2ab2c

h. (5x2y + 7) (–x + 2y)⋅= -5x3y + 10x2y2 + (-7x) + 14y

i. (3x2 + 5x – 9) . (x2 + 3x + 2)= 3x4 + 9x3 + 6x2 + 5x3 + 15x2 + 10x - 9x2 - 27x - 18= 3x4 + 14x3 + 12x2 – 17x -18

j. (a + 2ab + 3b) . (a + b)= a2 + 2a2b + 3ab + ab + 2ab2 + 3b2

= a2 + 2a2b + 4ab + 2ab2 + 3b2

4. Selesaikan bentuk-bentuk berikut.a. (x + 2y)2

= (x + 2y) (x + 2y) = x2 + 2xy + 2xy + 4y2

= x2 + 4xy + 4yb. (2x – y)2

= (2x - y) (2x - y)= 4x2 - 2xy - 2xy + y2

= 4x2 - 4xy + y2

c. (–3a + 2b)3

= 9a2 - 6ab - 6ab + 4b2 (-3a + 2b)= (9a2 – 12ab + 4b2) (-3a + 2b)= -27a3 + 36 a2b - 12ab2 + 18a2b - 24 ab2 + 8b3

= -27a3 + 54a2b – 36 ab2 + 8b3

d. (4p – 2q)4

= 16p2 - 8pq - 8pq + 4q2

= (16p2 - 16pq + 4q2) (4p - 2q)2

= 256p4 – 256p3q + 64p2q2 – 256p3q + 256p2q2 – 64pq3 + 64p2q2 – 64pq3 + 16q4

= 256p4 – 500p3q + 384 p2q2 – 128pq3 + 16q4

e. (a + 2b + 3c)2

= a2 + 4b2 + 9c2 + 4ab + 6ac + 12bcf. (3p + q – 5r)3

= 27p3 + 125r3 + 27p2q – 135p2r + 6pq2 - 90pqr + 75pr2 + 75qr2 – 10q2rg. -(4a + b)2

= 16a2 + 8ab + b2

h. (3p + q)3

= 27p3 + 27p2q + 9pq2 + q3

i. (x + 2y + 1)4

j. (3a + 2b – c)

5. Selesaikan bentuk-bentuk berikut.a. (8a + 4) : 4 b. (–12xy + 9y) : 3y c. (4xy2 + 2x2y) : 2y d. (–2ab2 + 3a2b3) : 2ab

e. (–12x2y2z + 16xy2z) : xy2zf. (20p3q2r – 15pqr3 + 10qr) : 5pqg. (p2 + 2q) : 2h. (6a2bc) : 3abci. (–20a3b7c5) : 2ab2c3

j. (36x4yz) : 9x2y