(-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+28β56z+28minus, 56, z, plus, 28.
Hint #22 / 7
Expression: \dfrac{1}{2}\cdot(-28z+14) Β
2
1
Β
β
(β28z+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}} Β
2
1
Β
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} Β
2
1
Β
β
(β28z+14)
( Β
2
1
Β
Γβ28z)+( Β
2
1
Β
Γ14)
β14z+7
Β
Β
=
?
β56z+28
=
?
β56z+28
ξ
Β
=β56z+28
Β
Β
No, \dfrac{1}{2}\cdot(-28z+14) Β
2
1
Β
β
(β28z+14)start fraction, 1, divided by, 2, end fraction, dot, left parenthesis, minus, 28, z, plus, 14, right parenthesis is not equivalent to -56z+28β56z+28minus, 56, z, plus, 28.
Hint #33 / 7
Expression: (-1.4z+0.7)\times40(β1.4z+0.7)Γ40left 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} Β
(β1.4z+0.7)Γ40
40(β1.4z+0.7)
(40Γβ1.4z)+(40Γ0.7)
β56z+28
Β
Β
=
?
β56z+28
=
?
β56z+28
=
?
β56z+28
=
β
β56z+28
Β
Β
Yes, (-1.4z+0.7)\times40(β1.4z+0.7)Γ40left parenthesis, minus, 1, point, 4, z, plus, 0, point, 7, right parenthesis, times, 40 is equivalent to -56z+28β56z+28minus, 56, z, plus, 28.
Hint #44 / 7
Expression: (14-7z)\cdot(-4)(14β7z)β
(β4)left parenthesis, 14, minus, 7, z, right parenthesis, dot, left parenthesis, minus, 4, right parenthesis
Let's distribute the \blueD{-4}β4start 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} Β
(14β7z)β
(β4)
β4(14β7z)
(β4Γ14)+(β4Γβ7z)
β56+28z
Β
Β
=
?
β56z+28
=
?
β56z+28
=
?
β56z+28
ξ
Β
=β56z+28
Β
Β
No, (14-7z)\cdot(-4)(14β7z)β
(β4)left parenthesis, 14, minus, 7, z, right parenthesis, dot, left parenthesis, minus, 4, right parenthesis is not equivalent to -56z+28β56z+28minus, 56, z, plus, 28.
Hint #55 / 7
Expression: (8z-4)(-7)(8zβ4)(β7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis
Let's distribute the \blueD{-7}β7start 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} Β
(8zβ4)(β7)
β7(8zβ4)
(β7Γ8z)+(β7Γβ4)
β56z+28
Β
Β
=
?
β56z+28
=
?
β56z+28
=
?
β56z+28
=
β
β56z+28
Β
Β
Yes, (8z-4)(-7)(8zβ4)(β7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis is equivalent to -56z+28β56z+28minus, 56, z, plus, 28.
Hint #66 / 7
Expression: -2(-28z-14)β2(β28zβ14)minus, 2, left parenthesis, minus, 28, z, minus, 14, right parenthesis
Let's distribute the \blueD{-2}β2start 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} Β
β2(β28zβ14)
(β2Γβ28z)+(β2Γβ14)
56z+28
Β
Β
=
?
β56z+28
=
?
β56z+28
ξ
Β
=β56z+28
Β
Β
No, -2(-28z-14)β2(β28zβ14)minus, 2, left parenthesis, minus, 28, z, minus, 14, right parenthesis is not equivalent to -56z+28β56z+28minus, 56, z, plus, 28.
Hint #77 / 7
The following expressions are equivalent to -56z+28β56z+28minus, 56, z, plus, 28:
(-1.4z+0.7)\times40(β1.4z+0.7)Γ40left parenthesis, minus, 1, point, 4, z, plus, 0, point, 7, right parenthesis, times, 40
(8z-4)(-7)(8zβ4)(β7)left parenthesis, 8, z, minus, 4, right parenthesis, left parenthesis, minus, 7, right parenthesis
