Question

utilizando o conceito de "Produtos Notáveis", calcule:
a) (x²+3)²
b) (4x-7)²
c) (2x-3y)²
d) (9-5t)²
e) (3x-5)(3x+5)
h) (8+5x)(8-5x)
g) (6x+2y)(6x-2y)

Answer 1

a) (x²)² + 2.x².3 + 3² = x^4 + 6x² + 9 

b) (4x)² + 2.4x.(-7) + (-7)² = 16x² - 56x + 49 

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

d) 9² + 2.9.(-5t) + (-5t)² = 81 - 90t + 25t² = 25t² - 90t + 81

e) (3x)² - ( 5)² = 9x² - 25

f) (8)² - (5x)² = 64 + 25x² = 25x² - 64 

g) (6x)² - (2y)² = 36x² - 4y²                                   ok

Answer 2

a)

Formula:

(a + b)² = a² + 2ab + b²

(x² +3)² = (x² )² + 2x²*3 + 3²

= x^(4) + 6x² + 9
__________

b)

(a - b)² = a² - 2ab + b²

(4x - 7)² = (4x)² -2×4x×7 + 7²

= 16x² - 56x + 49
________


c)

(a -b)² = a² - 2ab + b²

(2x - 3y)² = (2x)² - 2×2x×3y + (3y)²

= 4x² - 12xy + 9y²
________

d)

(a -b)² = a² - 2ab + b²

(9-5t)² = 9² -2×9×5t + (5t)²

= 81 - 90t + 25t²
________

e)

(a - b)(a + b) = a² - b²

(3x - 5)(3x + 5) = (3x)² - 5²

= 9x² - 25
________

h)

(a + b)(a - b) = a² - b²

(8x + 5)(8x -5) = (8x)² - 5²

= 64x² - 25
________

g)

(a + b)(a - b) = a² - b²

(6x + 2y)(6x - 2y) = (6x)² - (2y)²

= 36x² - 4y²