Question

Fatore os trinômios quadrados perfeitos a seguir.

a) x² + 2xy + y² =

b) a² + 2ab + b² =

c) x² + 4x + 4 =

d) x² + 6x + 9 =

e) 4x² - 12xy + 9y² =​

Answer 1

Explicação passo-a-passo:

===> a² + 2ab + b² = (a + b)²

===> a² - 2ab + b² = (a - b)²

a) x² + 2xy + y²

=> (x)² + 2.(x).(y) + (y)²

=> (x + y).(x + y)

=> (x + y)²

b) a² + 2ab + b²

=> (a)² + 2.(a).(b) + (b)²

=> (a + b).(a + b)

=> (a + b)²

c) x² + 4x + 4

=> (x)² + 2.(4).(x) + 4

=> (x)² + 2.(2).(x) + (2)²

=> (x + 2).(x + 2)

=> (x + 2)²

d) x² + 6x + 9

=> (x)² + 2.(6).(x) + 9

=> (x)² + 2.(2.3).(x) + (3)²

=> (x)² + 2.(3).(x) + (3)²

=> (x + 3).(x + 3)

=> (x + 3)²

e) 4x² - 12xy + 9y²

=> (2x)² - 2.(12xy) + (3y)²

=> (2x)² - 2.(6.2.x.y) + (3y)²

=> (2x)² - 2.(2.3).(2x).(y) + (3y)²

=> (2x)² - 2.(2x).(3y) + (3y)²

=> (2x - 3y).(2x - 3y)

=> (2x - 3y)²