Question

Vă rog sa ma ajutati cu acest exercitiu

Answer 1

Răspuns:

Explicație pas cu pas:

4x^2y^2 - 3y^2 = y^2 * (4x^2 - 3) = y^2 * (2x - √3) * (2x + √3)

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2ax^2 - a = a(2x^2 - 1) = a(x√2 - 1)(x√2 + 1)

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t^2/9 - 5t^2x^2 = t^2(1/9 - 5x^2) = t^2(1/3 - x√5)(1/3 + x√5)

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3x^2 - 12x^2y^2z^2 = 3x^2(1 - 4y^2z^2) = 3x^2(1 - 2yz)(1 + 2yz)

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(x + 2)^2 - (x - 2)^2 = (x + 2 + x - 2)(x + 2 -x + 2) = 8x

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a^2 - (a - 3)^2 = (a + a - 3)(a - a + 3) = 3(2a - 3)

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4a^2 - (2a - 1)^2 = (2a + 2a - 1)(2a -2a + 1) = 4a - 1

Answer 2

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 )