Matematika

Pertanyaan

tolong donk bantu saya mengerjakannya
tolong donk bantu saya mengerjakannya

1 Jawaban

  • 28. 2(3x - 5)² = 2.(3x - 5)(3x - 5) = 2((3x.3x) + (3x.(-5)) + ((-5).3x) + ((-5).(-5)))
                           = 2((3.3.x¹⁺¹) + (-15x) + (-15x) + 25) = 2(9x² - 15x - 15x + 25)
                           = 2(9x² - 30x +25) = 2.9x² - 2.30x + 2.25
                           = 18x² - 60x + 50, Jawabannya (D)

    29. (2a + 3)² - (a - 4)² = ((2a + 3)(2a + 3)) - ((a - 4)(a - 4))
                                         = ((2.2a¹⁺¹) + (2a.3) + (3.2a) + (3.3)) - ((a¹⁺¹) + (a.(-4)) +
                                            ((-4)a) + ((-4).(-4))
                                         = (4a² + 6a + 6a + 9) - (a² + (-4a) + (-4a) + 16)
                                         = (4a² + 12a + 9) - (a² - 4a - 4a + 16)
                                         = (4a² + 12a + 9) - (a² - 8a + 16)
                                         = 4a² + 12a + 9 - a² -(-8a) - 16
                                         = 4a² + 12a + 9 - a² + 8a - 16
                                         = 4a² - a² + 12a + 8a + 9 -16
                                         = 3a² + 20a + (-7) = 3a² + 20a - 7, Jawabannya (D)

    30. (2a + 3b)³ = (2a + 3b)(2a + 3b)(2a + 3b)
                             = ((2a.2a) + (2a.3b) + (3b.2a) + (3b.3b)).(2a + 3b)
                             = ((2.2a¹⁺¹) + (2.3.a.b) + (3.2.a.b) + (3.3.b¹⁺¹)).(2a + 3b)
                             = (4a² + 6ab + 6ab + 9b²).(2a + 3b)
                             = (4a² + 12ab + 9b²).(2a + 3b)
                             = (4a².2a) + (4a².3b) + (12ab.2a) + (12ab. 3b) + (9b².2a) +
                                (9b².3b)
                             = (4.2a²⁺¹) + (4.3a².b) + (12.2.a¹⁺¹.b) + (12.3.a.b¹⁺¹) + (9.2.b².a) +
                                 (9.3.b²⁺¹)
                             = 8a³ + 12a²b + 24a²b + 36ab² + 18ab² + 27b³
                             = 8a³ + 36a²b + 54ab² + 27b³, jawaban D

    31. (3p - 2q)⁴ = (3p - 2q).(3p - 2q).(3p - 2q).(3p - 2q)
                            = ((3p.3p) + (3p.(-2q)) + ((-2q).3p) + ((-2q).(-2q))).((3p.3p) +
                               (3p.(-2q)) + ((-2q).3p) + ((-2q).(-2q)))     
                            = ((3.3p¹⁺¹) + (3.2p.(-q)) + ((-2).3.q.p) + ((-2).(-2)q¹⁺¹)).((3.3p¹⁺¹) +
                               (3.2p.(-q)) + ((-2).3.q.p) + ((-2).(-2)q¹⁺¹))
                            = (9p² + (-6pq) + (-6pq) + 4q²).(9p² + (-6pq) + (-6pq) + 4q²)
                            = (9p² - 6pq - 6pq + 4q²).(9p² - 6pq - 6pq + 4q²)
                            = (9p² - 12pq + 4q²).(9p² - 12pq + 4q²)
                            = (9p².9p²) + (9p².(-12pq)) + (9p².4q²) + ((-12pq).9p²) +
                               ((-12pq).(-12pq)) + ((-12pq).4q²) + (4q².9p²) + (4q².(-12pq)) +
                               (4q².4q²)
                            = (9.9p²⁺²) + (9.(-12)p²⁺¹q) + (9.4p²q²) + ((-12).9.p²⁺¹.q) +
                               ((-12).(-12)p¹⁺¹q¹⁺¹) + ((-12).4.p.q¹⁺²) + (4.9.q²p²) +
                               (4.(-12).p.q²⁺¹) + (4.4q²⁺²)                       
                            = 81p⁴ + (-108p³q) + 36p²q² + (-108p³q) + 144p²q² + (-48pq³) +
                               36p²q² + (-48pq³) + 16q⁴
                            = 81p⁴ - 108p³q + 36p²q² - 108p³q + 144p²q² - 48pq³ + 36p²q² -
                               48pq³ + 16q⁴
                            = 81p⁴ - 108p³q - 108p³q + 36p²q² + 144p²q² + 36p²q² - 48pq³ -
                               48pq³ + 16q⁴
                            = 81p⁴ - 216 p³q + 216p²q² - 96pq³ + 16q⁴, jawaban (C)

    Maaf kalau jawabannya panjang dan lama, karena kakak menjabarkannya secara detail.