Question

ILL GIVE 100 POINTS PLS ANSWER QUICK
Simplify negative two thirds times m times quantity negative four sevenths times m minus one fifth end quantity.

negative 8 over 21 times m squared minus 2 over 15 times m
8 over 21 times m squared plus 2 over 15 times m
negative 8 over 21 times m squared plus 2 over 15 times m
8 over 21 times m squared plus one fifth

Answer 1

Answer:

$\dfrac{8}{21}m^2+\dfrac{2}{15}m$

Step-by-step explanation:

Given expression:

$-\dfrac{2}{3}m\left(-\dfrac{4}{7}m-\dfrac{1}{5}\right)$

Apply the distributive law  a(b - c) = ab - ac :

$\implies \left(-\dfrac{2}{3}m\right)\cdot \left(-\dfrac{4}{7}m\right)-\left(-\dfrac{2}{3}m\right)\cdot \left(\dfrac{1}{5}\right)$

Apply the rule  -(-a) = a :

$\implies \dfrac{2}{3}m\cdot\dfrac{4}{7}m+\dfrac{2}{3}m\cdot \dfrac{1}{5}$

$\implies \dfrac{2}{3}\cdot\dfrac{4}{7} \cdot m \cdot m+\dfrac{2}{3}\cdot \dfrac{1}{5}\cdot m$

$\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\cdot\dfrac{b}{d}=\dfrac{ab}{cd}:$

$\implies \dfrac{2\cdot 4}{3\cdot 7} \cdot m \cdot m+\dfrac{2\cdot 1}{3\cdot 5} \cdot m$

Simplify:

$\implies \dfrac{8}{21}m^2+\dfrac{2}{15}m$