Question

Utilizando a regra de produto notáveis, escreva o desenvolvimento de cada item:

a) (x + 1)2 =_______________________
b) (2x + 3)2 =_______________________
c) (2x + 3y)2 =_______________________
d) (5a + x)2 =_______________________
e) (3a – 1)2 = _______________________
f) (3m – 5n)2 =_______________________
g) (2x – 3y)2 =_______________________
h) (a2 – b3)2 =_______________________

Answer 1

Explicação passo-a-passo:

.

$a)(x + 1) {}^{2}$

$x {}^{2} + 2x \times 1 + 1 {}^{2}$

$x {}^{2} + 2x + 1$

.

$b)(2x + 3) {}^{2}$

$(2x) {}^{2} + 2 \times 2x \times 3 + 3 {}^{2}$

$4x {}^{2} + 12x + 9$

.

$c)(2x + 3y) {}^{2}$

$(2x) {}^{2} + 2 \times 2x \times 3y + (3y) {}^{2}$

$4x {}^{2} + 12xy + 9y {}^{2}$

.

$d)(5a + x) {}^{2}$

$(5a) {}^{2} + 2 \times 5ax + x {}^{2}$

$25a {}^{2} + 10ax + x {}^{2}$

.

$e)(3a - 1) {}^{2}$

$(3a) {}^{2} - 2 \times 3a \times 1 + 1 {}^{2}$

$9a {}^{2} - 6a + 1$

.

$f)(3m - 5n) {}^{2}$

$(3m) {}^{2} - 2 \times 3m \times 5n + (5n) {}^{2}$

$9m {}^{2} - 30mn + 25n {}^{2}$

.

$g)(2x - 3y) {}^{2}$

$(2x) {}^{2} - 2 \times 2x \times 3y + (3y) {}^{2}$

$4x {}^{2} - 12xy + 9y {}^{2}$

.

$h)(a {}^{2} - b {}^{3} ) {}^{2}$

$(a {}^{2} ) {}^{2} - 2a {}^{2} b {}^{3} + (b {}^{3} ) {}^{2}$

$a {}^{4} - 2a {}^{2} b {}^{3} + b {}^{6}$