Quadrilateros exercicios resolvidos 8 ano

a)  (3x + y)²

= (3x + y)²

= (3x)² + 2.3x.y + y² = 9x² + 6xy + y²

b)  (2x + 3y)³

= (2x + 3y)³

= (2x)³ + 3.(2x)².3y + 3.2x.(3y)² + (3y)³

= 8x³ + 36x²y + 54xy² + 27y³

c)  (5 + x)²

= (5 + x)²

= 5² + 2.5.x + x²

= 25 + 10x + x²

  d)  (x – y)² – (x + y)²

primeiramente:

(x – y)² = x² – 2xy + y²

(x + y)² = x² + 2xy + y².

assim,

(x – y)² – (x + y)²

= x² – 2xy + y² – (x² + 2xy + y²)

= x² – 2xy + y² – x² – 2xy – y²

= x² – x² – 2xy – 2xy + y² – y²

= -2xy – 2xy

= -4xy

e)    (x – – 5)

= (x – -5)

= xx + x(-5) + (-2)x + (-)

=  x² + ) + (-5))x + (-)

= x² – 7x + 10

f)  (x + – 4)

= (x + 15)(x – 4)

=  xx + x(-4) + 15x + 15(-4)

= x² + (15 + (-4))x + )

= x² + 11x – 60