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Estudos Gerais03/27/2025

1) Fatore por agrupamento as seguintes expressões algébricas...

  1. Fatore por agrupamento as seguintes expressões algébricas:

a) αx + by + ay + bx ax + by + ay + bx = ax + ay + bx + by = = a (x + y) + b (x + y) = = (a + b) (x + y)

b) αx - y - x + ay ax - y - x + ay = ax + ay - (x + y) = = a (x + y) - (x + y) = = (x + y) (a - 1)

c) a²b + a² + 5ab³ + 5b² a²b + a² + 5ab + 5b = = a² (ab + 1) + 5b² (ab + 1) = = (a² + 5b²) (ab + 1)

1) Fatore por agrupamento as seguintes expressões algébricas:

a) αx + by + ay + bx
ax + by + ay + bx = ax + ay + bx + by =
= a (x + y) + b (x + y) =
= (a + b) (x + y)

b) αx - y - x + ay
ax - y - x + ay = ax + ay - (x + y) =
= a (x + y) - (x + y) =
= (x + y) (a - 1)

c) a²b + a² + 5ab³ + 5b²
a²b + a² + 5ab + 5b =
= a² (ab + 1) + 5b² (ab + 1) =
= (a² + 5b²) (ab + 1)
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