Question

1-Desenvolva algebricamente cada quadrado da soma de dois termos.
(a) (x+5)²
(b) 7a+1)²
(c)x+2y)²
(d)(x²+1)²
(e)(x+5)²
(f)(6+x)²
(g)(2x+xy)²
(h)(x²+1)²
(i)(x+2y)²
(j)(x³+1/3)²

Answer 1

Resposta:

(a) (x+5)² = x² + 2.x.5 + 5² = x² + 10x + 25

(b) (7a+1)² = (7a)² + 2.7a.1 + 1² = 49a² + 14a +1

(c) (x+2y)² = x² + 2.x.2y + (2y)² = x² + 4xy + 4y²

(d) (x²+1)²  = (x²)² + 2.x².1 + 1² = x⁴ +2x² + 1

(e) (x+5)² = x² + 2.x.5 + 5² = x² + 10x + 25

(f) (6+x)² = 6² + 2.6.x + x² = 36 + 12x + x²

(g) (2x+xy)² = (2x)² + 2.2x.xy + (xy)² = 4x² + 4x²y + x²y²

(h) (x²+1)² = (x²)² + 2.x².1 + 1² = x⁴ +2x² + 1

(i) (x+2y)² = x² + 2.x.2y + (2y)² = x² + 4xy + 4y²

(j) (x³+1/3)² =

$(x^{3} +\frac{1}{3} )^{2} =(x^{3} )^{2} +2.x^{3} .\frac{1}{3} +(\frac{1}{3} )^{2} =~~~~x^{6} +\frac{2x^{3} }{3} +\frac{1}{9}$