Question

responder pordutos notaveis

Answer 1

Explicação passo-a-passo:

a)

$\sf (x-13)^2=x^2-2\cdot x\cdot13+13^2$

$\sf (x-13)^2=\red{x^2-26x+169}$

b)

$\sf (7+3x)^2=7^2+2\cdot7\cdot3x+(3x)^2$

$\sf (7+3x)^2=\red{49+42x+9x^2}$

c)

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

$\sf (a^2+4b^3)\cdot(a^2-4b^3)=\red{a^4-16b^6}$

d)

$\sf \left(\dfrac{x}{6}+3\right)\cdot\left(\dfrac{x}{6}-3\right)=\left(\dfrac{x}{6}\right)^2-3^2$

$\sf \left(\dfrac{x}{6}+3\right)\cdot\left(\dfrac{x}{6}-3\right)=\red{\dfrac{x^2}{36}-9}$

e)

$\sf (15m+2)^2=(15m)^2+2\cdot15m\cdot2+2^2$

$\sf (15m+2)^2=\red{225m^2+60m+4}$

f)

$\sf (x^2z-y^3)^2=(x^2z)^2-2\cdot x^2zy^3+(y^3)^2$

$\sf (x^2z-y^3)^2=\red{x^4z^2-2x^2zy^3+y^6}$

e)

$\sf \left(\dfrac{3}{9}+x\right)^2=\left(\dfrac{3}{9}\right)^2+2\cdot\dfrac{3}{9}\cdot x+x^2$

$\sf \left(\dfrac{3}{9}+x\right)^2=\red{\dfrac{9}{81}+\dfrac{6x}{9}+x^2}$

f)

$\sf \left(3x^3-\dfrac{4}{3}\right)^2=(3x^3)^2-2\cdot3x^3\cdot\dfrac{4}{3}+\left(\dfrac{4}{3}\right)^2$

$\sf \left(3x^3-\dfrac{4}{3}\right)^2=\red{9x^6-8x^3+\dfrac{16}{9}}$

g)

$\sf (12+b^3)\cdot(12-b^3)=12^2-(b^3)^2$

$\sf (12+b^3)\cdot(12-b^3)=\red{144-b^6}$

h)

$\sf (20x^2+6y)\cdot(20x^2-6y)=(20x^2)^2-(6y)^2$

$\sf (20x^2+6y)\cdot(20x^2-6y)=\red{400x^4-36y^2}$