Question

Descompuneți în factori:

a) (x²+3x+1)²-1

b) (2m-3)(m-1)²-4(2m-3)

c) (p-3)(p²+1)+2p(p-3)

d) (3a-1)²-25

e) (x+2)²-(3-2x)²

f) ($\frac{1}{2} a + \frac{3}{2}b$)²-($\frac{3}{2}a - \frac{1}{2}b$)²

Answer 1

a) (x² + 3x + 1 - 1)(x² + 3x + 1 + 1)= (x² + 3x)(x² + 3x + 2) = x(x + 3)(x² + 3x + 2)

b) (2m-3)(m-1)²-4(2m-3) = (2m - 3)[(m - 1)² - 4] = (2m - 3)(m - 1 + 2)(m - 1 - 2) = (2m - 3)(m + 1)(m - 3)

c) (p - 3)(p² + 1 + 2p) = (p - 3)(p + 1)²

d) (3a - 1 + 5)(3a - 1 - 5) = (3a + 4)(3a - 6) = 3(3a + 4)(a - 2)

e) (x + 2 - 3 + 2x)(x + 2 + 3 - 2x) = (3x - 1)(5 - x)

f) (a/2 + 3b/2 - 3a/2 + b/2)(a/2 + 3b/2 + 3a/2 - b/2) = (4b/2 - 2a/2)(4a/2 + 2b/2) = (2b - a)(2a + b)