Matematika

Pertanyaan

Ubahlah menjadi suku-suku (1+x)2(1+y)2-(x+y)2-(xy-1)2+x-y

1 Jawaban

  • (1 + x)× 2(1 + y)× 2 -(x + y)× 2 -(xy - 1)× 2 + x - y
    = (1 + x)× 4(1 + y) - (x + y)× 2 - (xy - 1)× 2 + x - y
    = (4 + 4x) × (1 + y) - (x + y)× 2 - (xy - 1)× 2 + x - y
    = 4 + 4y + 4x + 4xy - (x + y)× 2 - (xy - 1)× 2 + x - y
    = 4 + 4y + 4x + 4xy + (-x - y)× 2 +(-xy + 1)× 2 + 1x - 1y
    = 4 + (4 - 1)y + (4 + 1)x + 4xy + (-x - y)× 2 +(-xy + 1)× 2
    = 4 + 3y + 5x + 4xy + (-x - y)× 2 +(-xy + 1)× 2
    = 4 + 3y + 5x + 4xy - x × 2 - y × 2 - xy × 2 + 2
    = 4 + 3y + 5x + 4xy - 2x - 2y - 2xy + 2
    = 4 + (3 - 2)y + (5 - 2)x + 4xy - 2xy + 2
    = 4 + 1y + 3x + 4xy - 2xy + 2
    = 4 + y + 3x + 4xy - 2xy + 2
    = 6 + y + 3x + (4 - 2)xy
    = 6 + y + 3x + 2xy

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