Question

which expression is equivalent to $9q^{2}-\frac{2}{3}(3q - 7)+5q^{2}$?
a $9q^{2}-\frac{5}{3}q - 3$
b $9q^{2}-2q - 3$
c $14q^{2}-2q+\frac{14}{3}$
d $14q^{2}-\frac{5}{3}q-\frac{14}{3}$

Explanation:

Step1: Expand el término $\frac{2}{3}(3q - 7)$

$\frac{2}{3}(3q - 7)=\frac{2}{3}\times3q-\frac{2}{3}\times7 = 2q-\frac{14}{3}$

Step2: Reescribir la expresión original

$9q^{2}-\frac{2}{3}(3q - 7)+5q^{2}=9q^{2}-(2q - \frac{14}{3})+5q^{2}$

Step3: Combinar términos semejantes

$(9q^{2}+5q^{2})-2q+\frac{14}{3}=14q^{2}-2q+\frac{14}{3}$

Answer:

C. $14q^{2}-2q+\frac{14}{3}$