Atividade

Exemplos :

1) (5 + x)² = 5² + 2.5.x + x² = 25 + 10x + x²

2) (2x + 3y)² = (2x)² + 2.(2x).(3y) + (3y)² = 4x² + 12xy + 9y²

Exercícios

1) Depois de ver os exemplos, calcule:

a) (3 + x)² = ( R: 9 + 6x +x²)b) (x + 5)² = ( R: x² + 10x + 25)
c) ( x + y)² = ( R: x² + 2xy +y²)
d) (x + 2)² = ( R: x² + 4x + 4)
e) ( 3x + 2)² = ( R: 9x² + 12x +4)
f) (2x + 1)² = (R: 4x² + 4x + 1)
g) ( 5+ 3x)² = (R: 25 + 30x + 9x²)
h) (2x + y)² = (R: 4x² + 4xy + y²)
i) (r + 4s)² = (R: r² + 8rs + 16s²)j) ( 10x + y)² = (R: 100x² + 20xy + y²)l) (3y + 3x)² = (R: 9y² + 18xy + 9x²)m) (-5 + n)² = (R: 25 -10n + n²)
n) (-3x + 5)² = (R: 9x² - 30x + 25)
o) (a + ab)² = (R: a² + 2a²b + a²b²)
p) (2x + xy)² = (R: 4x² + 4x²y + x²y²)
q) (a² + 1)² = (R: (a²)² + 2a² + 1)r) (y³ + 3)² = [R: (y³)² + 6y³ + 9]s) (a² + b²)² = [R: (a²)² + 2a²b² + (b²)²]
t) ( x + 2y³)² = [R: x² + 4xy³ + 4(y³)²]
u) ( x + ½)² = (R: x² +x + 1/4)
v) ( 2x + ½)² = (R: 4x² + 2x + 1/4)x) ( x/2 +y/2)² = [R: x²/4 + 2xy/4 + y²/4]
Exemplos:
1)( 3 – X)² = 3² + 2.3.X + X² = 9– 6x + x²

2) (2x -3y)² = (2x)² -2.(2x).(3y) + (3y)² = 4x² - 12xy+ 9y²


Exercícios

2) Calcule:

a) ( 5 – x)² = (R: 25 – 10x + x²)b) (y – 3)² = (R: y² - 6y + 9)c) (x – y)² = (R: x² - 2xy + y²)
d) ( x – 7)² = (R: x² - 14x + 49)e) (2x – 5) ² = (R: 4x² - 20 x + 25)f) (6y – 4)² = (R: 36y² - 48y + 16)
g) (3x – 2y)² = (R: 9x² - 12xy + 4y²)h) (2x – b)² = (R: 4x² - 4xb + b²)
i) (5x² - 1)² = [R: 25(x²)² - 10x² + 1)
j) (x² - 1)² =  (R: x⁴ - 2x² + 1)                       
l) (9x² - 1)² = (R:  81x⁴- 18x² + 1)
m) (x³ - 2)² = (R:  x⁶ - 4x³ + 4)