Question

Completeaza:
a)4×3^6+7×3^7=(.....)^2

b) 4×5^20+9×5^21=(....)^2

c)2^10+3×2^10+5×4^5=(...)^2

Dau coroana.

Answer 1

a)4×3^6+7×3^7=(.....)^2

4×3^6+7×3x3^6 = 3^6 x (4 + 7 x 3) = (3^3)^2 x25=27^2 x 5^2 = (3^3x5)^2

b) 4×5^20+9×5^21=(....)^2

4×5^20+9×5x5^20 = 5^20x(4+45) = (5^10)^2x7^2 =  (7x5^10)^2

c)2^10+3×2^10+5×4^5=(...)^2

4x2^10 + 5×4^5 = 2^2x 2^10 + 2^2 x 5 x 4^4 = 2^2x(2^10 + 5x2^8) = 2^2x(2^8x(4+5)) = 2^2x2^8x3^2 = 2^10x3^2 = (2^5x3)^2