Question

16. Fatore os trinômios quadrados perfeitos

a) x² + 6x + 9
b) 4x² + 12xy + 9y²
c) x$^{4}$ - 4x² + 4
d) x²y² - 10xy + 25
e) $\frac{4}{9} x^{2} + \frac{4}{21} x + \frac{1}{49}$

Answer 1

Explicação passo-a-passo:

a)

x² + 6x + 9

= x² + 2.x.3 + 3²

= (x + 3)²

b)

4x² + 12xy + 9y²

= (2x)² + 2.2x.3y + (3y)²

= (2x + 3y)²

c)

x⁴ - 4x² + 4

= (x²)² - 2.x².2 + 2²

= (x² - 2)²

d)

x²y² - 10xy + 25

= (xy)² - 2.xy.5 + 5²

= (xy - 5)²

e)

$\sf \dfrac{4x^2}{9}+\dfrac{4x}{21}+\dfrac{1}{49}$

$\sf =\Big(\dfrac{2x}{3}\Big)^2+2\cdot\dfrac{2x}{3}\cdot\dfrac{1}{7}+\Big(\dfrac{1}{7}\Big)^2$

$\sf =\red{\Big(\dfrac{2x}{3}+\dfrac{1}{7}\Big)^2}$