Question

Dau coroana! scrie sub cea mai simpla forma, următoarele expresii algebrice:
(doar b, c, e, f, g)


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Answer 1

Explicație pas cu pas:

b) E(x) = ( x - 3 )( x + 3 ) - ( x - 4 )²

E(x) = x² - 9 - ( x² - 8x + 16 )

E(x) = x² - 9 - x² + 8x - 16  = - 9 + 8x - 16 = - 25 + 8x

E(x) = - 25 + 8x

- pentru subpunctul b) am folosit formulele de calcul prescurtat:

• ( a - b )( a + b ) = a² - b²;
• ( a - b )² = a² - 2ab + b²;

c) E(x) = ( 2x - 5 )² + ( x + 1 )² - ( x√5 + 3 )( x√5 - 3 )

E(x) = 4x² - 20x + 25 + x² + 2x + 1 - ( x√5 + 3 )( x√5 - 3 )

E(x) = 4x² - 20x + 25x + x² + 2x + 1 - ( 5x² - 9 )

E(x) = 4x² - 20x + 25 + x² + 2x + 1 - 5x² + 9

E(x) = 0 - 20x + 25 + 2x + 1 + 9 = 0 - 18x + 35 = - 18x + 35

E(x) = - 18x + 35

e) E(x) = 3( x - √2 )( x + √2 ) - ( x + √2 )² - ( x - √2 )²

E(x) = 3( x² - 2 ) - ( x² + 2√2x + 2 ) - ( x² - 2√2x + 2 )

E(x) = 3x² - 6 - x² - 2√2x - 2 - x² + 2√2x - 2

E(x) = 3x² - 6 - x² - 2 - x² - 2

E(x) = x² - 10

f) E(x) = ( x² - 2 )² - ( x - 1 )( x + 1 )( x² + 1 ) + 4( x - 3 )²

E(x) = x⁴ - 4x² + 4 - ( x² - 1 )( x² + 1 ) + 4( x² - 6x + 9 )

E(x) = x⁴ - 4x² + 4 - ( x⁴ - 1 ) + 4x² - 24x + 36

E(x) = x⁴ - 4x² + 4 - x⁴ + 1 + 4x² - 24x + 36

E(x) = - 4x² + 4 + 1 + 4x² - 24x + 36 = 4 + 1 - 24x + 36 = 41 - 24x

E(x) = 41 - 24x

g) E(x) = ( x + 2 )( x² + 4 )( x - 2 ) - ( 2 - x² )²

E(x) = ( x² - 4 )( x² + 4 ) - ( 4 - 4x² + x⁴ )

E(x) = x⁴ - 16 - 4 + 4x² - x⁴ = - 16 - 4 + 4x² = - 20 + 4x²

E(x) = - 20 + 4x²

#copaceibrainly