Question

3-desenvolva os produtos notáveis ⚠️​

Answer 1

Resposta:

a) $x^{2} - 6x+9$

b) $a^{2} - 8a + 16$

c) $y^{2} - 10y + 25$

d) $m^{2} - 12m + 36$

e) $4x^{2} - 12x + 9$

f) $a^{2} - 8ab + 16b^{2}$

g) $25x^{2} - 30x + 9$

h) $9a^{2} - 12ab + 4b^{2}$

Explicação passo-a-passo:

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

a)

$(x-3)^{2} =\\ x^{2} - 2*x*3+3^{2} \\x^{2} - 6x+3^{2} \\x^{2} - 6x+9$

b)

$(a-4)^{2} =\\a^{2} - 2*a*4 + 4^{2} \\a^{2} - 8a + 4^{2}\\a^{2} - 8a + 16$

c)

$(5-y)^{2} =\\5^{2} - 2*5*y + y^{2} \\5^{2} - 10y + y^{2} \\25 - 10y + y^{2}$→ $y^{2} - 10y + 25$

d)

$(m-6)^{2} =\\m^{2} - 2*m*6 + 6^{2} \\m^{2} - 12m + 6^{2}\\m^{2} - 12m + 36$

e)

$(2x-3)^{2} =\\(2x)^{2} - 2*2x*3 + 3^{2} \\4x^{2} - 2*2x*3 + 3^{2}\\4x^{2} - 12x + 3^{2}\\4x^{2} - 12x + 9$

f)

$(a-4b)^{2} =\\a^{2} - 2*a*4b + (4b)^{2} \\a^{2} - 8ab + (4b)^{2} \\a^{2} - 8ab + 16b^{2}$

g)

$(5x-3)^{2} =\\(5x)^{2} - 2*5x*3 + 3^{2} \\25x^{2} - 2*5x*3 + 3^{2}\\25x^{2} - 30x + 3^{2}\\25x^{2} - 30x + 9$

h)

$(3a-2b)^{2} =\\(3a)^{2} - 2*3a*2b + (2b)^{2} \\9a^{2} - 2*3a*2b + (2b)^{2}\\9a^{2} - 12ab + (2b)^{2}\\9a^{2} - 12ab + 4b^{2}$