VALENDO 30 PONTOS!!!!
Calcule os quadrados.
a) (x - y) ²
b) (a - 2) ²
c) (x - 1) ²
d) (3a - 5) ²
e) (5 - 4a) ²
f) (3x - 2y) ²
g) (3a² - 5) ²
h) (x - 1/2) ²
j) (3m - n/5) ²
Calcule as expressões.
a) (2x+1)² + (x - 5)²
b) (x-1)² - (x+1)²
c) x(x-3)² - 4 (x+1/2)²
d) (x-3)² - (x-2)² + (x+3)(x-1)
Soluções para a tarefa
a)
= (x - y) ²
= x² - 2xy + y²
b)
= (a - 2) ²
= a² - 2.2a + 4
= a² - 4a + 4
c)
= (x - 1) ²
= x² - 2.1x + 1
= x² - 2x + 1
d)
= (3a - 5) ²
= (3a)² - 2.5.3a + 25
= 9a² - 30a + 25
e)
= (5 - 4a) ²
= 25 - 2.5.4a + (4a)²
= 25 - 40a + 16a²
= 16a² - 40a + 25
f)
= (3x - 2y) ²
= (3x)² - 2.3x.2y + (2y)²
= 9x² - 12xy + 4y²
********************************
g)
= (3a² - 5) ²
= (3a²)² - 2.3a².5 + 25
= 9a⁴ - 30a² + 25
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
h)
= (x - 1/2) ²
= x² - 2.1 . x + 1
---- ------
2 4
= x² - x + 1
----
4
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
j)
= (3m - n/5) ²
(3m)² - 2. 3m . n + (n)²
---- ------
5 (5)²
9m² - 6mn + n²
-------- -----
5 25
**************************************
Calcule as expressões.
a)
= (2x + 1)² + (x - 5)²
= (2x)² + 2.2x.1 + 1 + x² - 2.5x + 25
= 4x² + 4x + 1 + x² - 10x + 25
= 4x² + x² + 4x - 10x + 1 + 25
= 5x² - 6x + 26
**********************************
b)
= (x - 1)² - (x + 1)²
= x² - 2.1.x + 1 - (x² + 2.1.x + 1)
= x² - 2x + 1 - (x² + 2x + 1)
= x² - 2x + 1 - x² - 2x - 1
= x² - x² - 2x - 2x + 1 - 1
= - 4x
****************************
c)
= x(x - 3)² - 4 (x + 1/2)²
= x.(x² - 2.3x + 9) - 4.(x² + 2.1.x + 1 )
--- ----
2 4
= x.(x² - 6x + 9) - 4.(x² + x + 1 )
----
4
= x³ - 6x² + 9x - 4x² - 4x - 4.(1/4)
= x³ - 10x² + 5x - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
= (x - 3)² - (x - 2)² + (x + 3).(x - 1)
= x² - 2.3x + 9 - (x² - 2.2x + 4) + x² - x + 3x - 3
= x² - 6x + 9 - (x² - 4x + 4) + x² + 2x - 3
= x² - 6x + 9 - x² + 4x - 4 + x² + 2x - 3
= x² - x² - 6x + 4x + 2x + 9 - 4 + x² - 3
= 9 - 4 + x² - 3
= 5 + x² - 3
= 2 + x²
= x² + 2
*********************
Resposta:
Calcule os quadrados.
a)
= (x - y) ²
= x² - 2xy + y²
b)
= (a - 2) ²
= a² - 2.2a + 4
= a² - 4a + 4
c)
= (x - 1) ²
= x² - 2.1x + 1
= x² - 2x + 1
d)
= (3a - 5) ²
= (3a)² - 2.5.3a + 25
= 9a² - 30a + 25
e)
= (5 - 4a) ²
= 25 - 2.5.4a + (4a)²
= 25 - 40a + 16a²
= 16a² - 40a + 25
f)
= (3x - 2y) ²
= (3x)² - 2.3x.2y + (2y)²
= 9x² - 12xy + 4y²
********************************
g)
= (3a² - 5) ²
= (3a²)² - 2.3a².5 + 25
= 9a⁴ - 30a² + 25
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
h)
= (x - 1/2) ²
= x² - 2.1 . x + 1
---- ------
2 4
= x² - x + 1
----
4
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
j)
= (3m - n/5) ²
(3m)² - 2. 3m . n + (n)²
---- ------
5 (5)²
9m² - 6mn + n²
-------- -----
5 25
**************************************
Calcule as expressões.
a)
= (2x + 1)² + (x - 5)²
= (2x)² + 2.2x.1 + 1 + x² - 2.5x + 25
= 4x² + 4x + 1 + x² - 10x + 25
= 4x² + x² + 4x - 10x + 1 + 25
= 5x² - 6x + 26
**********************************
b)
= (x - 1)² - (x + 1)²
= x² - 2.1.x + 1 - (x² + 2.1.x + 1)
= x² - 2x + 1 - (x² + 2x + 1)
= x² - 2x + 1 - x² - 2x - 1
= x² - x² - 2x - 2x + 1 - 1
= - 4x
****************************
c)
= x(x - 3)² - 4 (x + 1/2)²
= x.(x² - 2.3x + 9) - 4.(x² + 2.1.x + 1 )
--- ----
2 4
= x.(x² - 6x + 9) - 4.(x² + x + 1 )
----
4
= x³ - 6x² + 9x - 4x² - 4x - 4.(1/4)
= x³ - 10x² + 5x - 1
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
= (x - 3)² - (x - 2)² + (x + 3).(x - 1)
= x² - 2.3x + 9 - (x² - 2.2x + 4) + x² - x + 3x - 3
= x² - 6x + 9 - (x² - 4x + 4) + x² + 2x - 3
= x² - 6x + 9 - x² + 4x - 4 + x² + 2x - 3
= x² - x² - 6x + 4x + 2x + 9 - 4 + x² - 3
= 9 - 4 + x² - 3
= 5 + x² - 3
= 2 + x²
= x² + 2
*********************
Explicação passo-a-passo: