Question

Alguém me ajuda, por favor!!! Valendo 20 Pontos.

Calcule o quadrado das expressões algébricas.

a) (y - y^2)^2
b) (4 - m^2)^2
c) (1/2 x - √2)^2
d) (2 - √2)^2
e) (7b - 1)^2
f) (10 - 4n)^2
g) (√7 - 5)^2

Answer 1

$(a-b)^2=a^2-2ab+b^2$

a)
$(y - y^2)^2=\\y^2-2y.y^2+(y^2)^2=\\y^2-2y^3+y^4$

b)
$(4 - m^2)^2=\\4^2-2.4m^2+(m^2)^2=\\16-8m^2+m^4$

c)
$( \frac{1}{2x} - \sqrt{2} )^2=\\( \frac{1}{2x})^2-2. \frac{1}{2x} \sqrt{2}+( \sqrt{2} )^2=\\ \frac{1}{2^2x^2}- \frac{2 \sqrt{2} }{2x}+ \sqrt{2^2}=\\ \frac{1}{4x^2}- \frac{\sqrt{2} }{x}+2$

d)
$(2 - \sqrt{2} )^2=\\2^2-2.2 \sqrt{2}+( \sqrt{2} )^2=\\4-4 \sqrt{2}+2=\\6-4 \sqrt{2}$

e)
$(7b - 1)^2=\\(7b)^2-2.7b.1+1^2=\\49b^2-14b+1$

f)
$(10 - 4n)^2=\\10^2-2.10.4n+(4n)^2=\\100-80n+16n^2$

g)
$( \sqrt{7} - 5)^2=\\( \sqrt{7})^2-2 \sqrt{7}.5+5^2=\\7-10 \sqrt{7}+25=\\32-10 \sqrt{7}$