Question

4. Descompuneţi in factori a) x³ + x² - xy² - y²; c) a³ + 2a²-4a-8; b) a³ + a²-4a-4; d) x²a-x²b + b-a.​

Answer 1

Răspuns:

a) x³ + x² - xy² - y² = (x + 1)(x - y)(x + y)  

b) a³ + a²- 4a - 4 = (a + 1)(a - 2)(a + 2)  

c) a³ + 2a²-4a-8 = (a + 2)(a - 2)(a + 2)

d) x²a-x²b + b-a = (a - b)(x - 1)(x + 1)

Explicație pas cu pas:

a)

x³ + x² - xy² - y² =

x² × (x + 1) - y² × (x + 1) =

(x + 1)(x² - y²) =

(x + 1)(x - y)(x + y)  

b)

a³ + a² - 4a - 4 =

a² × (a + 1) - 4 × (a + 1) =

(a + 1)(a² - 4) =

(a + 1)(a - 2)(a + 2)  

c)

a³ + 2a² - 4a - 8 =

a² × (a + 2) - 4 × (a + 2) =

(a + 2)(a² - 4) =

(a + 2)(a - 2)(a + 2)

d)

x²a - x²b + b - a =​

x² × (a - b) - (a - b) =

(a - b) (x² - 1) =

(a - b)(x - 1)(x + 1)