Question

Dezvoltați următoarele expresii algebrice:
a) (3x + 1)²; b) (2a + 3b)²;
c) (5a - 2b)²; d) (4u + 3v)².,
e) (4xy – 3z)?; f) (4xy + 32)².​

Answer 1

Răspuns:

(a + b)² = a² + 2 × a × b + b²

(a - b)² = a² - 2 × a × b + b²

a)

(3x + 1)² = (3x)² + 2 × 3x × 1 + 1² = 9x² + 6x + 1

b)

(2a + 3b)² = (2a)² + 2 × 2a × 3b + (3b)² = 4a² + 12ab + 9b²

c)

(5a - 2b)² = (5a)² - 2 × 5a × 2b  + (2b)² = 25a² - 20ab + 4b²

d)

(4u + 3v)² = (4u)² + 2 × 4u × 3v + (3v)² = 16u² + 24uv + 9v²

e)

(4xy – 3z)² = (4xy)² - 2 × 4xy × 3z + (3z)² = 16x²y² - 24xyz + 9z²

f)

(4xy + 32)² = (4xy)² + 2 × 4xy × 32 + 32² = 16x²y² + 256xy + 1024

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