which expressions are equivalent to -90 - 60w? choose 3 answers: a -30(3 + 2w) b (-9 - 6w)·10 c -3(30 - 20w)…
which expressions are equivalent to -90 - 60w? choose 3 answers: a -30(3 + 2w) b (-9 - 6w)·10 c -3(30 - 20w) d (6 + 4w)×15 e -20(4.5 + 3w)
Answer
Answer:
A. $-30(3 + 2w)$, B. $(-9 - 6w)\cdot10$, E. $-20(4.5 + 3w)$
Explanation:
Step1: Expand option A
[ \begin{align*} -30(3 + 2w)&=-30\times3-30\times2w\ &=-90 - 60w \end{align*} ]
Step2: Expand option B
[ \begin{align*} (-9 - 6w)\cdot10&=-9\times10-6w\times10\ &=-90 - 60w \end{align*} ]
Step3: Expand option C
[ \begin{align*} -3(30 - 20w)&=-3\times30+(-3)\times(-20w)\ &=-90 + 60w \end{align*} ]
Step4: Expand option D
[ \begin{align*} (6 + 4w)\times15&=6\times15+4w\times15\ &=90 + 60w \end{align*} ]
Step5: Expand option E
[ \begin{align*} -20(4.5 + 3w)&=-20\times4.5-20\times3w\ &=-90 - 60w \end{align*} ]