Question

(X-1/2)^2-(1/2)^2
(3/4-x)^2-1/16
(3a-1/3x)^2-4/9 x^2

Answer 1

Vom utiliza formula:

→ a²-b²=(a-b)(a+b)

Rezolvare:

→ (x-1/2)²-(1/2)²=(x-1/2-1/2)(x-1/2+1/2)=x(x-1)=x²-x

→ (3/4-x)²-1/16=(3/4-x)²-(1/4)²=(3/4-x-1/4)(3/4-x+1/4)=(1/2-x)(1-x)=1/2-x/2-x+x²=1/2-3x/2+x²

→ (3a-1/3x)²-4/9 x²=(3a-1/3x)²-(2x/3)²=(3a-1/3x-2x/3)(3a-1/3 x+2x/3)=(3a-x)(3a+x/3)=9a²+3ax/3-3ax-x²/3=9a²+ax-3ax-x²/3=9a²-2ax-x²/3

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PS: Este mai simpla rezolvarea in acest fel decat daca am desface parantezele de la inceput.