Question

Jabarkan bentuk perkalian berikut dengan menggunakan skema,kemudian sederhanakan

A.(2x+3)(x-4)
B(a+3b)(a-5b)
C.(5m-1)(2m+4)
D .(a-3)(a²+4a+5)
E.(x+y)(3x²+xy+2y²
F.(3k-5)(k²+2k-6)
G(a+ab+b)(a-b)
H.(x²+3x-5)(x²-2x-1)

Answer 1

A. (2x + 3)(x-4) = (2x. x) + ( 2x. (-4)) + (3 × x ) + ( 3 × (-4))
= 2x² - 8x + 3x - 12 = 2x² - 5x - 12

b. (a +3b)(a-5b) = a² - 5ab + 3ab - 15b² = a² -2ab - 15ab²

c. (5m-1)(2m+4) = 10m² + 20m - 2m + 4
= 10m² + 18m + 4 = 2(5m² + 9m + 2)

d. (a-3)(a² +4a+5) = a³ + 4a² + 5a - 3a² - 12a - 15 = a³ + a² - 7a - 15 = a(a² +a - 7) - 15

e. (x+y)(3x² +xy + 2y²) = 3x³ + x²y + 2xy² + 3x²y + xy² + 2y³ = 3x³ + 4x²y + 3xy² + 2y³ = 3x (x² + y²) + 2y(2x² + y²)

f. (3k-5)(k²+2k-6) = 3k³ +6k²-18k -5k² - 10k + 30 = 3k³ +k² -28k + 30 = k²(3k+1) + 2(-14k+15)

g. (a +ab+b)(a-b) = a² - ab + a²b - ab² + ab - b² = a² + a²b - ab² - b²

h. (x² +3x -5)(x²-2x-1) = x⁴ - 2x³ - x² + 3x³ - 6x² - 3x - 5x² + 10x + 5 = x⁴ + x³ -12x² + 7x + 5