Which expressions are equivalent to -56z+28? choose 2 answers:

(-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

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