Question

1- Desenvolva os produtos:
a)
$(7x + 8y) {}^{2}$
b)
$(6a - 5b) {}^{2}$
c)
$(11x + 10y) \times (11x - 10y)$
d)
$(4m + 6n) { }^{3}$
e)
$(5p - 7q) {}^{3}$
​

Answer 1

Resposta:

$a) \: {(7x + 8y)}^{2} \\ 49 {x}^{2} + 112xy + 64 {y}^{2}$

$b) \: {(6a - 5b)}^{2} \\ 36 {a}^{2} - 60ab + 25 {b}^{2}$

$c) \: (11x + 10y) \times (11x - 10y) \\ 121 {x}^{2} - 110xy + 110xy - 10 0{y}^{2} \\ 121 {x}^{2} - 100 {y}^{2}$

$d) \: {(4m + 6n)}^{3} \\( 4 {m})^{3} + 3 \times ( {4m})^{2} \times 6n + 3 \times 4m \times {(6n)}^{2} + {(6n)}^{3} \\ 64 {m}^{3} + 3 \times 16 {m}^{2} \times 6n + 3 \times 4n \times 36 {n}^{2} + 216 {n}^{3} \\ 64 {m}^{3} + 288 {m}^{2} n + 432 {mn}^{2} + 216 {n}^{3}$

$e) \: ( {5p - 7q)}^{3} \\ {(5p)}^{3} - 3 \times {(5p)}^{2} \times 7q + 3 \times 5p \times {(7q)}^{2} - {(7q)}^{3} \\ 125 {p}^{3} - 3 \times 25 {p}^{2} \times 7q + 3 \times 5p \times 49 {q}^{2} - 343 {q}^{3} \\ 125 {p}^{3} - 525 {p}^{2} q + 735 {pq}^{2} - 343 {q}^{3}$