QuestionFind expressions equivalent to $4(-5 n+4)-5 n$ . Options include: $-5(4 n+4)-5 n$ , $16 n-25$ , $-25 n+4$ , $4(-7 n+2 n+4)-5 n$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $4(-5 n+4)-5 n$ . . We need to find the expressions that are equivalent to the given expression.

STEP 2

First, we need to simplify the given expression. We can do this by using the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, a(b + c) = ab + ac.
$4(-5 n+4)-5 n =4 \cdot (-5n) +4 \cdot4 -5n$

STEP 3

Now, perform the multiplication.
$(-5 n+)-5 n = -20n +16 -5n$

STEP 4

Combine like terms.
$-20n +16 -n = -25n +16$

STEP 5

Now, we will compare this simplified expression with the provided options.
Option1 $-5(4 n+4)-5 n$
First, simplify this expression using the distributive property and combining like terms.
$-5(4 n+4)-5 n = -5 \cdot4n -5 \cdot4 -5n = -20n -20 -5n = -25n -20$ This expression is not equivalent to the given expression.

STEP 6

Option2 $16 n-25$
This expression is not equivalent to the given expression.

STEP 7

Option3 $-25 n+4$
This expression is not equivalent to the given expression.

STEP 8

Option4 $4(-7 n+2 n+4)-5 n$
First, simplify this expression using the distributive property and combining like terms.
$4(-7 n+2 n+4)-5 n =4 \cdot (-7n) +4 \cdot2n +4 \cdot4 -5n = -28n +8n +16 -5n = -25n +16$ This expression is equivalent to the given expression.
So, the expressions equivalent to $4(-5 n+4)-5 n$ are $-25n +16$ and $4(-7 n+2 n+4)-5 n$ .

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QuestionFind expressions equivalent to $4(-5 n+4)-5 n$ . Options include: $-5(4 n+4)-5 n$ , $16 n-25$ , $-25 n+4$ , $4(-7 n+2 n+4)-5 n$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $4(-5 n+4)-5 n$ . . We need to find the expressions that are equivalent to the given expression.

STEP 2

First, we need to simplify the given expression. We can do this by using the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, a(b + c) = ab + ac.
$4(-5 n+4)-5 n =4 \cdot (-5n) +4 \cdot4 -5n$

STEP 3

Now, perform the multiplication.
$(-5 n+)-5 n = -20n +16 -5n$

STEP 4

Combine like terms.
$-20n +16 -n = -25n +16$

STEP 5

STEP 6

Option2 $16 n-25$
This expression is not equivalent to the given expression.

STEP 7

Option3 $-25 n+4$
This expression is not equivalent to the given expression.

STEP 8

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QuestionFind expressions equivalent to 4(−5n+4)−5n4(-5 n+4)-5 n4(−5n+4)−5n. Options include: −5(4n+4)−5n-5(4 n+4)-5 n−5(4n+4)−5n, 16n−2516 n-2516n−25, −25n+4-25 n+4−25n+4, 4(−7n+2n+4)−5n4(-7 n+2 n+4)-5 n4(−7n+2n+4)−5n.

Studdy Solution

STEP 1

Assumptions1. The given expression is 4(−5n+4)−5n4(-5 n+4)-5 n4(−5n+4)−5n. . We need to find the expressions that are equivalent to the given expression.

STEP 2

STEP 3

Now, perform the multiplication.(−5n+)−5n=−20n+16−5n(-5 n+)-5 n = -20n +16 -5n(−5n+)−5n=−20n+16−5n

STEP 4

Combine like terms.−20n+16−n=−25n+16-20n +16 -n = -25n +16−20n+16−n=−25n+16

STEP 5

STEP 6

Option2 16n−2516 n-2516n−25This expression is not equivalent to the given expression.

STEP 7

Option3 −25n+4-25 n+4−25n+4This expression is not equivalent to the given expression.

STEP 8

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QuestionFind expressions equivalent to $4(-5 n+4)-5 n$ . Options include: $-5(4 n+4)-5 n$ , $16 n-25$ , $-25 n+4$ , $4(-7 n+2 n+4)-5 n$ .

Assumptions1. The given expression is $4(-5 n+4)-5 n$ . . We need to find the expressions that are equivalent to the given expression.

Now, perform the multiplication.
$(-5 n+)-5 n = -20n +16 -5n$

Combine like terms.
$-20n +16 -n = -25n +16$

Option2 $16 n-25$
This expression is not equivalent to the given expression.

Option3 $-25 n+4$
This expression is not equivalent to the given expression.