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Calcul algébrique

Factorisation d'expressions
Correction exercice seconde

Factoriser les expressions suivantes.
  • A = 4x²(2x + 2)² - 16x²

    A = 4x2(2x + 2)2 - 16x2
    A = [2x(2x + 2) - 4x][2x(2x + 2) + 4x]
    A = (4x2 + 4x - 4x)(4x2 + 4x + 4x)
    A = 4x2(4x2 + 8x)


  • B = (5x - 2)³ - (2 - 5x)² - (2 - 5x)(3x - 3)

    B = (5x - 2)3 - (2 - 5x)2 - (2 - 5x)(3x - 3)
    B = (-1)3(2 - 5x)3 - (2 - 5x)2 - (2 - 5x)(3x - 3)
    B = (2 - 5x)[ - (2 - 5x)2 - (2 - 5x) - (3x - 3)]
    B = (2 - 5x)[ - (4 - 20x + 25x2) - 2 + 5x - 2x + 3]
    B = (2 - 5x)( - 4 + 20x - 25x2 + 3x + 1)
    B = (2 - 5x)( - 25x2 + 23x - 3)


  • C = 25x² - 1 - (4x - 3)(5x + 1)

    C = 25x2 - 1 - (4x - 3)(5x + 1)
    C = (5x - 1)(5x + 1) - (4x - 3)(5x + 1)
    C = (5x + 1)[(5x - 1) - (4x - 3)]
    C = (5x + 1)(5x - 1 - 4x + 3)
    C = (5x + 1)(x + 2)


  • D = (3x - 1)² - (6x + 2)²

    D = (3x - 1)2 - (6x + 2)2
    D = [(3x - 1) + (6x + 2)][(3x - 1) - (6x + 2)]
    D = (3x - 1 + 6x + 2)(3x - 1 - 6x - 2)
    D = (9x + 1)( - 3x - 3)


  • E = 9x² - 30x + 25

    E = 9x2 - 30x + 25
    Identité remarquable.
    E = (3x - 5)2


Factorisation d'expressions - Exercices de maths seconde - Factorisation d'expressions
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