Răspuns:
Explicație pas cu pas:
a² - b² = ( a - b ) ( a + b) → formula folosita
a) 4 x² y² - 3 y² = y²(4 x² - 3) = y² (2 x - √3) ( 2 x + √3)
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b) 2 a x² - a = a(2x² - 1 ) = a(√2 x - 1 ) ( √2 x + 1 )
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c) t²/9 - 5 t² x² = t²(1/9 - 5 x²) = t² ( 1/3 - √5 x ) ( 1/3 + √5 x )
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d) 3 x² - 12 x² y² z² = 3 x²( 1 - 4 y² z² ) = 3 x² ( 1 - 2 y z ) ( 1 + 2 y z )
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e) ( x + 2)² - ( x - 2 )² = (x+2-x+2)(x+2+x-2) = 4 · 2 x = 8 · x
-> folosesc formula a² - b² = ( a - b ) ( a + b); unde a = x + 2 si b = x - 2
Sau:
= x² + 4 x + 4 - ( x² - 4 x + 4 ) =
= x² + 4 x + 4 - x² + 4 x - 4 =
= 8 · x
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f) a² - ( a - 3 )² = a² - ( a² - 6 a + 9 ) = a² - a² + 6 a - 9 = 6 a - 9 = 3(2 a+3)
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g) 4 a² - ( 2 a - 1 )² = ( 2 a - 2 a + 1 ) ( 2 a + 2 a - 1 ) = 1·(4 a + 1 )
sau:
= 4 a² - ( 4 a² - 4 a + 1 ) =
= 4 a² - 4 a² + 4 a - 1 =
= 1 ×( 4 a - 1 )
