Question

produtos notáveis, resolva:

a) x² - (x +y)²
b) (2x+7)²
c) (9x+1) (9x-1)
d) (3y-5)²
e) (a-4y)²
f) (x-y)²
g) (ab+a) (ab-a)
h) (2x+3xy)²
i) (10x-ab)²
j) (x-4) (x+4)
k) (x+2) (x-2)​

Answer 1

Resposta:

$a) \: {x}^{2} - {(x + y)}^{2} \\ {x}^{2} - ( {x}^{2} + 2xy + {y}^{2} ) \\ {x}^{2} - {x}^{2} - 2xy - {y}^{2} \\ - 2 {y}^{2} - {y}^{2}$

$b) \: {(2x + 7)}^{2} \\ 4 {x}^{2} + 28x + 49$

$c) \: (9x + 1) \times (9x - 1) \\ 81 {x}^{2} - 9x + 9x - 1 \\ 81 {x}^{2} - 1$

$d) \: {(3y - 5)}^{2} \\ 9 {y}^{2} - 30y + 25$

$e) \: {(a - 4y)}^{2} \\ {a}^{2} - 8ay + 16$

$f) \: {(x - y)}^{2} \\ {x}^{2} - 2xy + {y}^{2}$

$g) \: (ab + a) \times (ab - a) \\ {(ab)}^{2} - {a}^{2} b + {a}^{2} b - {a}^{2} \\ {a}^{2} {b}^{2} - {a}^{2}$

$h) \: {(2x + 3xy)}^{2} \\ 4 {x}^{2} + 12 {x}^{2} y + 9 {x}^{2} {y}^{2}$

$i) \: {(10x - ab)}^{2} \\ 100 {x}^{2} - 10abx + {a}^{2} {b}^{2}$

$j) \: (x - 4) \times (x + 4) \\ {x}^{2} + 4x - 4x + 16 \\ {x}^{2} + 16$

$k) \: (x + 2) \times (x - 2) \\ {x}^{2} - 2x + 2x - 4 \\ {x}^{2} - 4$