Answer:
(-1.4z+0.7) x40 and (8z-4)(-7)
Step-by-step explanation:
Let's use the distributive property to expand each expression and see if it is equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #22 / 7
Expression: \dfrac{1}{2}\cdot(-28z+14)
2
1
⋅(−28z+14)start fraction, 1, divided by, 2, end fraction, dot, left parenthesis, minus, 28, z, plus, 14, right parenthesis
Let's distribute the \blueD{\dfrac{1}{2}}
2
1
start color #11accd, start fraction, 1, divided by, 2, end fraction, end color #11accd to each of the terms inside of the parentheses.
\begin{aligned} \blueD{\dfrac{1}{2}}\cdot(-28z+14)&\stackrel{?}=-56z+28\\\\ \left(\blueD{\dfrac{1}{2}}\times-28z\right)+\left(\blueD{\dfrac{1}{2}}\times14\right)&\stackrel{?}=-56z+28\\\\ -14z+7&\neq -56z+28\end{aligned}
2
1
⋅(−28z+14)
(
2
1
×−28z)+(
2
1
×14)
−14z+7
=
?
−56z+28
=
?
−56z+28
=−56z+28
No, \dfrac{1}{2}\cdot(-28z+14)
2
1
⋅(−28z+14)start fraction, 1, divided by, 2, end fraction, dot, left parenthesis, minus, 28, z, plus, 14, right parenthesis is not equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #33 / 7
Expression: (-1.4z+0.7)\times40(−1.4z+0.7)×40left parenthesis, minus, 1, point, 4, z, plus, 0, point, 7, right parenthesis, times, 40
Let's distribute the \blueD{40}40start color #11accd, 40, end color #11accd to each of the terms inside of the parentheses.
\begin{aligned} (-1.4z+0.7)\times\blueD{40}&\stackrel{?}=-56z+28\\\\ \blueD{40}(-1.4z+0.7)&\stackrel{?}=-56z+28\\\\ (\blueD{40}\times-1.4z)+(\blueD{40}\times0.7)&\stackrel{?}=-56z+28\\\\ -56z+28&\stackrel{\checkmark}{=} -56z+28\end{aligned}
(−1.4z+0.7)×40
40(−1.4z+0.7)
(40×−1.4z)+(40×0.7)
−56z+28
=
?
−56z+28
=
?
−56z+28
=
?
−56z+28
=
✓
−56z+28
Yes, (-1.4z+0.7)\times40(−1.4z+0.7)×40left parenthesis, minus, 1, point, 4, z, plus, 0, point, 7, right parenthesis, times, 40 is equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #44 / 7
Expression: (14-7z)\cdot(-4)(14−7z)⋅(−4)left parenthesis, 14, minus, 7, z, right parenthesis, dot, left parenthesis, minus, 4, right parenthesis
Let's distribute the \blueD{-4}−4start color #11accd, minus, 4, end color #11accd to each of the terms inside of the parentheses.
\begin{aligned} (14-7z)\cdot(\blueD{-4})&\stackrel{?}=-56z+28\\\\ \blueD{-4}(14-7z)&\stackrel{?}=-56z+28\\\\ (\blueD{-4}\times14)+(\blueD{-4}\times-7z)&\stackrel{?}=-56z+28\\\\ -56+28z&\neq -56z+28\end{aligned}
(14−7z)⋅(−4)
−4(14−7z)
(−4×14)+(−4×−7z)
−56+28z
=
?
−56z+28
=
?
−56z+28
=
?
−56z+28
=−56z+28
No, (14-7z)\cdot(-4)(14−7z)⋅(−4)left parenthesis, 14, minus, 7, z, right parenthesis, dot, left parenthesis, minus, 4, right parenthesis is not equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #55 / 7
Expression: (8z-4)(-7)(8z−4)(−7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis
Let's distribute the \blueD{-7}−7start color #11accd, minus, 7, end color #11accd to each of the terms inside of the parentheses.
\begin{aligned} (8z-4)(\blueD{-7})&\stackrel{?}=-56z+28\\\\ \blueD{-7}(8z-4)&\stackrel{?}=-56z+28\\\\ (\blueD{-7}\times8z)+(\blueD{-7}\times-4)&\stackrel{?}=-56z+28\\\\ -56z+28&\stackrel{\checkmark}{=} -56z+28\end{aligned}
(8z−4)(−7)
−7(8z−4)
(−7×8z)+(−7×−4)
−56z+28
=
?
−56z+28
=
?
−56z+28
=
?
−56z+28
=
✓
−56z+28
Yes, (8z-4)(-7)(8z−4)(−7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis is equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #66 / 7
Expression: -2(-28z-14)−2(−28z−14)minus, 2, left parenthesis, minus, 28, z, minus, 14, right parenthesis
Let's distribute the \blueD{-2}−2start color #11accd, minus, 2, end color #11accd to each of the terms inside of the parentheses.
\begin{aligned} \blueD{-2}(-28z-14)&\stackrel{?}=-56z+28\\\\ (\blueD{-2}\times-28z)+(\blueD{-2}\times-14)&\stackrel{?}=-56z+28\\\\ 56z+28&\neq -56z+28\end{aligned}
−2(−28z−14)
(−2×−28z)+(−2×−14)
56z+28
=
?
−56z+28
=
?
−56z+28
=−56z+28
No, -2(-28z-14)−2(−28z−14)minus, 2, left parenthesis, minus, 28, z, minus, 14, right parenthesis is not equivalent to -56z+28−56z+28minus, 56, z, plus, 28.
Hint #77 / 7
The following expressions are equivalent to -56z+28−56z+28minus, 56, z, plus, 28:
(-1.4z+0.7)\times40(−1.4z+0.7)×40left parenthesis, minus, 1, point, 4, z, plus, 0, point, 7, right parenthesis, times, 40
(8z-4)(-7)(8z−4)(−7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis
