Question

Use a regularidade que você acabou de ver e calcule em seu caderno estes produtos:


a) ( a+2) ( a-2)

b) ( y-4) ( y+4)

c) (x+3) ( x+3)

d) ( x-5) ( x+5)

e) ( a-1) (a+1)

f) ( t+6) ( t-6)

Answer 1

$a)~~ ( a+2) ( a-2)\to~~ a^2-\not2a+\not2a-4\to ~~ \boxed{a^2-4}\\\\\\\\ b) ( y-4) ( y+4)\to~~ y^2+\not4y-\not4y-16\to~~ \boxed{y^2-16}\\\\\\\\ c) ~~(x+3) ( x+3)\to~~ x^2+3x+3x+9\to~~ \boxed{x^2+6x+9}\\\\\\\\ d) ~~( x-5) ( x+5) \to~~ x^2+\not5x-\not5x-25\to~~ \boxed{x^2-25} \\\\\\\\ e) ~~( a-1) (a+1)\to~~a^2+\not a-\not a-1\to~~ \boxed{a^2-1}\\\\\\\\f) ~~( t+6) ( t-6)\to ~~ t^2-\not6t +\not6t-36\to~~ \boxed{t^2-36}$

Answer 2

modelo:

(a + b).(a - b) = a² - ab + ab - b² = a² - b²

a)
= ( a+ 2) ( a -2)
= a² - 2a + 2a - 4
= a² - 4

b)
( y - 4).( y + 4)
y² + 4y - 4y - 16
y² - 16

c)
=  (x + 3).( x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
--------------------------------------
= (x + 3).(x - 3)
= x² - 3x + 3x - 9
= x² - 9
-----------------------------------------
d)
= ( x - 5).( x + 5) 
= x² + 5x - 5x - 25
= x² - 25
-----------------------------------------
e)
= ( a - 1).(a + 1)
= a² + a - a - 1²
= a² - 1
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f)
= ( t + 6) ( t - 6)
= t² - 6t + 6t - 36
= t² - 36
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