Question

determine a forma mais simples de escrever:
a) (2a+b).(a-2b)
b) (a+x) .(a²-ax+x²)
c) (x-2).(x-3)-{(x-4).(x-s)}
d) (a-2b).{a.(b-3)+b.(1-a)}
e) (x-1).(x+1)+3(x-1).(x-1)+3.(x-1)+1

Answer 1

$a) \\ \\ (2a + b) * (a - 2b) \\ \\ 2a^2 - 4ab +ab - 2b^2 \\ \\ => 2a^2 - 3ab - 2b^2$

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$b) \\ \\ (a + x) *(a^2 -ax + x^2) \\ \\ a^3 -a^2x + ax^2 + a^2x - ax^2 + x^3 \\ \\ \\=> a^3 + x^3$

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$c) \\ \\ (x-2). \left \{(x-3)-((x-4).(x-s)) \right. \} \\ \\ x^2 - 3x - 2x + 6 - \left \{s(x-4)-(x^2 + 4x) \right. \} \\ \\ x^2 - 5x + 6 - \left \{s(x-4)-(x^2 + 4x) \right. \} \\ \\ => s(x + 4) - (9x - 6)$

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$d) \\ \\ (a-2b) * \left \{ {a.(b-3)+b.(1-a) \right.\} \\ \\ (a-2b) * \left \{ {a(b - 3) -(ab - b)\right.\} \\ \\ (a -2b) *(-3a +b) \\ \\ => -3a^2 + 7ab - 2b^2$

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$e) \\ \\ (x-1)*(x+1)+3(x-1)*(x-1)+3*(x-1)+1 \\ \\ x^2 - 1 + 3x^2 -6x + 3 + 3x + 3 + 1 \\ \\ x^2 - 1 + 3x^2 - 6x + 3x + 7 \\ \\ x^2 - 1 + 3x^2 - 3x + 7 \\ \\ => 4x^2 - 3x + 6$