Question

Resolva as operações indicadas e apresente a resposta na forma reduzida:

a) 2.(3y + 4)² - ( y +20) =

b) (5x + 3) ( 5x – 3) + 4(x – 3) =

c) (x + 4) ( x – 4) + 2(- x + 2) =

d) ( 2x + y)² - 2xy + y² - 2x² =

e) (x + 5)² - ( x – 6)² - 40 + x²

Answer 1

a
2[(3y)²+ 2 * 3y*4 + 4² ] - ( y + 20)
2( 9y² + 24y + 16) - y - 20 = 0
18y² + 48y + 32 - y - 20 = 0
18y² + 47y + 12 = 0 *****
b
[(5x)² - (3)² ] + 4x - 12 = 0
25x² - 9 + 4x - 12 = 0
25x² + 4x - 21 = 0 *****
c
[(x² ) - ( 4²)] - 2x + 4 = 0
x² - 16 - 2x + 4 = 0
x² - 2x - 12 = 0 *****
d
( 2x + y)² - 2xy  + y² - 2x²
[(2x)² + 2 *2x*y + y²]  - 2xy + y² - 2x² = 0
4x² +4xy + y² - 2xy + y² - 2x² = 0
2x² + 2xy + 2y² =0
x² + xy + y² = 0 ****

e
( x + 5 )² = x² + 2*x*5+ 5² = x² + 10x + 25 ***
( x - 6)² =  x² - 2 *x*6 + 6² = x² - 12x + 36 ***
reescrevendo
( x² + 10x + 25) - ( x² - 12x + 36 ) - 40 + x² = 0
x² + 10x + 25 - x² + 12x - 36 - 40 + x² = 0
x² + 22x - 51 = 0 ******