Question

*VALENDO 30 PONTOS*
Desenvolva os produtos notáveis​

Answer 1

Explicação passo-a-passo:

a)

$\sf (5x^2-y)^2=(5x^2)^2-2\cdot5x^2\cdot y+y^2$

$\sf (5x^2-y)^2=\red{25x^4-10x^2y+y^2}$

b)

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

$\sf (b-5)^2=\red{b^2-10b+25}$

c)

$\sf (p-8x)^2=p^2-2\cdot p\cdot8x+(8x)^2$

$\sf (p-8x)^2=\red{p^2-16px+64x^2}$

d)

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

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

e)

$\sf \left(\dfrac{m}{4}-3\right)^2=\left(\dfrac{m}{4}\right)^2-2\cdot\dfrac{m}{4}\cdot3+3^2$

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

f)

$\sf (5x-4)^2=(5x)^2-2\cdot5x\cdot4+4^2$

$\sf (5x-4)^2=\red{25x^2-40x+16}$

g)

$\sf (3x-2)^2=(3x)^2-2\cdot3x\cdot2+2^2$

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

h)

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

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

Answer 2

Oie, Td Bom?!

a)

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

$= (5x {}^{2} ) {}^{2} - 2 \: . \: 5x {}^{2} y + y {}^{2}$

$= 25x {}^{4} -1 0x {}^{2} y + y {}^{2}$

b)

$= (b - 5) {}^{2}$

$= b {}^{2} - 2b \: . \: 5 + 5 {}^{2}$

$= b {}^{2} - 10b + 25$

c)

$= (p - 8x) {}^{2}$

$= p {}^{2} - 2p \: . \: 8x + (8x) {}^{2}$

$= p {}^{2} - 16px + 64x {}^{2}$

d)

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

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

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

e)

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

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

$= \frac{m {}^{2} }{16} - \frac{6m}{4} + 9$

$= \frac{m {}^{2} }{16} - \frac{3m}{2} + 9$

f)

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

$= (5x) {}^{2} - 2 \: . \: 5x \: . \: 4 + 4 {}^{2}$

$= 25x {}^{2} - 40x + 16$

g)

$= (3x - 2) {}^{2}$

$= (3x) {}^{2} - 2 \: . \: 3x \: . \: 2 + 2 {}^{2}$

$= 9x {}^{2} - 12x + 4$

h)

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

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

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

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

Att. Makaveli1996