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QuestionChoose the equivalent expressions for (−2z−1)+(−5z−3)(-2z - 1) + (-5z - 3).

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to (−z−1)+(−5z−3)(- z-1)+(-5 z-3). Two expressions are equivalent if they simplify to the same result

STEP 2

First, let's simplify the given expression (−2z−1)+(−5z−)(-2 z-1)+(-5 z-).
To do this, we will combine like terms. The like terms here are the terms that contain zz and the constant terms.
(−2z−1)+(−5z−)=−2z−5z−1−(-2 z-1)+(-5 z-) = -2z -5z -1 -

STEP 3

Now, let's simplify the expression by adding the coefficients of the zz terms together and the constant terms together.
−2z−5z−1−3=−7z−-2z -5z -1 -3 = -7z -

STEP 4

Now, let's check the first expression (−2z−1)+(−3z−)(-2 z-1)+(-3 z-).
We will simplify this expression in the same way as we did for the given expression.
(−2z−1)+(−3z−)=−2z−3z−1−(-2 z-1)+(-3 z-) = -2z -3z -1 -

STEP 5

implify the expression by adding the coefficients of the zz terms together and the constant terms together.
−2z−3z−1−5=−5z−-2z -3z -1 -5 = -5z -This expression is not equivalent to −7z−4-7z -4, so it is not a correct answer.

STEP 6

Now, let's check the second expression −2z+−5z−3−1-2 z+-5 z-3-1.
We will simplify this expression in the same way as we did for the given expression.
−2z+−5z−3−1=−2z−5z−3−1-2 z+-5 z-3-1 = -2z -5z -3 -1

STEP 7

implify the expression by adding the coefficients of the zz terms together and the constant terms together.
−2z−5z−3−1=−7z−4-2z -5z -3 -1 = -7z -4This expression is equivalent to −7z−4-7z -4, so it is a correct answer.

STEP 8

Now, let's check the third expression (−z−2)+(−5z−3)(-z-2)+(-5 z-3).
We will simplify this expression in the same way as we did for the given expression.
(−z−2)+(−5z−3)=−z−5z−2−3(-z-2)+(-5 z-3) = -z -5z -2 -3

STEP 9

implify the expression by adding the coefficients of the zz terms together and the constant terms together.
−z−5z−2−3=−6z−5-z -5z -2 -3 = -6z -5This expression is not equivalent to −7z−4-7z -4, so it is not a correct answer.

STEP 10

Now, let's check the fourth expression −2z−4+−5z-2 z-4+-5 z.
We will simplify this expression in the same way as we did for the given expression.
−2z−4+−5z=−2z−5z−4-2 z-4+-5 z = -2z -5z -4

STEP 11

implify the expression by adding the coefficients of the zz terms together and the constant terms together.
−z−5z−4=−7z−4-z -5z -4 = -7z -4This expression is equivalent to −7z−4-7z -4, so it is a correct answer.
The expressions equivalent to (−z−)+(−5z−3)(- z-)+(-5 z-3) are −z+−5z−3−- z+-5 z-3- and −z−4+−5z- z-4+-5 z.

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