Question

me ajudeeeem pfvr desenvolva as expressoes a seguir: a)(p+q)² b)(3a+5b)² c)(7a+3b) d)(8a+3b) e)a/2+2b)² f)(1-3a)² g)(a³b²c-2)² h)(7ab - 2c)² i)(3/4x⁴-1)² J)(0,5A-0,2b)²

Answer 1

Explicação passo-a-passo:

a)

$\sf (p+q)^2=p^2+2\cdot p\cdot q+q^2$

$\sf (p+q)^2=p^2+2pq+q^2$

b)

$\sf (3a+5b)^2=(3a)^2+2\cdot3a\cdot5b+(5b)^2$

$\sf (3a+5b)^2=9a^2+30ab+25b^2$

c)

$\sf (7a+3b)^2=(7a)^2+2\cdot7a\cdot3b+(3b)^2$

$\sf (7a+3b)^2=49a^2+42ab+9b^2$

d)

$\sf (8a+3b)^2=(8a)^2+2\cdot8a\cdot3b+(3b)^2$

$\sf (8a+3b)^2=64a^2+48ab+9b^2$

e)

$\sf \left(\dfrac{a}{2}+2b\right)^2=\left(\dfrac{a}{2}\right)^2+2\cdot\dfrac{a}{2}\cdot2b+(2b)^2$

$\sf \left(\dfrac{a}{2}+2b\right)^2=\dfrac{a^2}{4}+2ab+4b^2$

f)

$\sf (1-3a)^2=1^2-2\cdot1\cdot3a+(3a)^2$

$\sf (1-3a)^2=1-6a+9a^2$

g)

$\sf (a^3b^2c-2)^2=(a^3b^2c)^2-2\cdot a^3b^2c\cdot2+2^2$

$\sf (a^3b^2c-2)^2=a^6b^4c^2-4a^3b^2c+4$

h)

$\sf (7ab-2c)^2=(7ab)^2-2\cdot7ab\cdot2c+(2c)^2$

$\sf (7ab-2c)^2=49a^2b^2-28abc+4c^2$

i)

$\sf \left(\dfrac{3x^4}{4}-1\right)^2=\left(\dfrac{3x^4}{4}\right)^2-2\cdot\dfrac{3x^4}{4}\cdot1+1^2$

$\sf \left(\dfrac{3x^4}{4}-1\right)^2=\dfrac{9x^8}{16}-\dfrac{3x^4}{2}+1$

j)

$\sf (0,5a-0,2b)^2=(0,5a)^2-2\cdot(0,5a)\cdot(0,2b)+(0,2b)^2$

$\sf (0,5a-0,2b)^2=0,25a^2-0,2ab+0,04b^2$