Question

*VALENDO 50 PONTOS*
Desenvolva os produtos notáveis ​

Answer 1

Explicação passo-a-passo:

a)

$\sf (a+1)\cdot(a+1)=a^2+a+a+1$

$\sf (a+1)\cdot(a+1)=\red{a^2+2a+1}$

b)

$\sf (2x+4)\cdot(2x-4)=(2x)^2-4^2$

$\sf (2x+4)\cdot(2x-4)=\red{4x^2-16}$

c)

$\sf \left(\dfrac{m}{4}-3)\cdot\left(\dfrac{m}{4}+3)=\left(\dfrac{m}{4}\right)^2-3^2$

$\sf \left(\dfrac{m}{4}-3)\cdot\left(\dfrac{m}{4}\right)=\red{\dfrac{m^2}{16}-9}$

d)

$\sf (m-2n)\cdot(m+2n)=m^2-(2n)^2$

$\sf (m-2n)\cdot(m+2n)=\red{m^2-4n^2}$

e)

$\sf (x^2y+4y)\cdot(x^2y-4y)=(x^2y)^2-(4y)^2$

$\sf (x^2y+4y)\cdot(x^2y-4y)=\red{x^4y^2-16y^2}$

f)

$\sf (5x-4)\cdot(5x+4)=(5x)^2-4^2$

$\sf (5x-4)\cdot(5x+4)=\red{25x^2-16}$

g)

$\sf (x+y)\cdot(x-y)=\red{x^2-y^2}$

h)

$\sf \left(xy-\dfrac{x}{2}\right)\cdot\left(xy+\dfrac{x}{2}\right)=(xy)^2-\left(\dfrac{x}{2}\right)^2$

$\sf \left(xy-\dfrac{x}{2}\right)\cdot\left(xy+\dfrac{x}{2}\right)=\red{x^2y^2-\dfrac{x^2}{4}}$

Answer 2

Oie, Td Bom?!

a)

$= (a + 1) \: . \: (a + 1)$

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

$= a {}^{2} + 2a \: . \: 1 + 1 {}^{2}$

$= a {}^{2} + 2a + 1$

b)

$= (2x + 4) \: . \: (2x - 4)$

$= (2x) {}^{2} - 4 {}^{2}$

$= 4x {}^{2} - 16$

c)

$= ( \frac{m}{4} - 3) \: . \: ( \frac{m}{4} + 3)$

$= ( \frac{m}{4} ) {}^{2} - 3 {}^{2}$

$= \frac{m {}^{2} }{16} - 9$

d)

$= (m - 2n) \: . \: (m + 2n)$

$= m {}^{2} - (2n) {}^{2}$

$= m {}^{2} - 4n {}^{2}$

e)

$= (x {}^{2} y + 4y) \: . \: (x {}^{2} y - 4y)$

$= (x {}^{2} y) {}^{2} - (4y) {}^{2}$

$= x { }^{4} y {}^{2} - 16y {}^{2}$

f)

$= (5x - 4) \: . \: (5x + 4)$

$= (5x) {}^{2} - 4 {}^{2}$

$= 25x {}^{2} - 16$

g)

$= (x + y) \: . \: (x - y)$

$= x {}^{2} - y {}^{2}$

h)

$= (xy - \frac{z}{2} ) \: . \: (xy + \frac{z}{2} )$

$= (xy) {}^{2} - ( \frac{z}{2} ){}^{2}$

$= x {}^{2} y {}^{2} - \frac{z {}^{2} }{4}$

Att. Makaveli1996