QuestionChoose the equivalent expressions for $-8(-2 s-4)$ . Options include:
1. $-8(-5 s+3 s-4)$
2. $-8(-8 s+6 s-4)$
3. $(-2 s-4) \cdot-8$
4. $16 s+32$

Studdy Solution

STEP 1

Assumptions1. The expressions are equivalent if they simplify to the same result. . The distributive property of multiplication over addition/subtraction is valid, which states that for all real numbers a, b, and c a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

First, let's simplify the given expression $-8(-2 s-4)$ using the distributive property.
$-8(-2 s-4) = -8 \cdot -2s + -8 \cdot -4$

STEP 3

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot - =16s +32$

STEP 4

Now, let's simplify the first candidate expression $-8(- s+3 s-4)$ .
$-8(- s+3 s-4) = -8 \cdot -2s + -8 \cdot -4$

STEP 5

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

STEP 6

The first candidate expression is equivalent to the given expression.

STEP 7

Now, let's simplify the second candidate expression $-(- s+6 s-4)$ .
$-(- s+6 s-4) = - \cdot -2s + - \cdot -4$

STEP 8

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

STEP 9

The second candidate expression is not equivalent to the given expression.

STEP 10

Now, let's simplify the third candidate expression $(-2 s-4) \cdot-8$ .
$(-2 s-4) \cdot-8 = -8 \cdot -2s + -8 \cdot -4$

STEP 11

Perform the multiplication.
$-8 \cdot -s + -8 \cdot -4 =16s +32$

STEP 12

The third candidate expression is equivalent to the given expression.

STEP 13

Now, let's compare the fourth candidate expression $16 s+32$ to the simplified given expression.
$16 s+32 =16s +32$

STEP 14

The fourth candidate expression is equivalent to the given expression.
The expressions equivalent to $-8(-2 s-4)$ are $-8(- s+3 s-4)$ , $(-2 s-4) \cdot-8$ , and $16 s+32$ .

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QuestionChoose the equivalent expressions for $-8(-2 s-4)$ . Options include:
1. $-8(-5 s+3 s-4)$
2. $-8(-8 s+6 s-4)$
3. $(-2 s-4) \cdot-8$
4. $16 s+32$

Studdy Solution

STEP 1

Assumptions1. The expressions are equivalent if they simplify to the same result. . The distributive property of multiplication over addition/subtraction is valid, which states that for all real numbers a, b, and c a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

First, let's simplify the given expression $-8(-2 s-4)$ using the distributive property.
$-8(-2 s-4) = -8 \cdot -2s + -8 \cdot -4$

STEP 3

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot - =16s +32$

STEP 4

Now, let's simplify the first candidate expression $-8(- s+3 s-4)$ .
$-8(- s+3 s-4) = -8 \cdot -2s + -8 \cdot -4$

STEP 5

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

STEP 6

The first candidate expression is equivalent to the given expression.

STEP 7

Now, let's simplify the second candidate expression $-(- s+6 s-4)$ .
$-(- s+6 s-4) = - \cdot -2s + - \cdot -4$

STEP 8

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

STEP 9

The second candidate expression is not equivalent to the given expression.

STEP 10

Now, let's simplify the third candidate expression $(-2 s-4) \cdot-8$ .
$(-2 s-4) \cdot-8 = -8 \cdot -2s + -8 \cdot -4$

STEP 11

Perform the multiplication.
$-8 \cdot -s + -8 \cdot -4 =16s +32$

STEP 12

The third candidate expression is equivalent to the given expression.

STEP 13

Now, let's compare the fourth candidate expression $16 s+32$ to the simplified given expression.
$16 s+32 =16s +32$

STEP 14

The fourth candidate expression is equivalent to the given expression.
The expressions equivalent to $-8(-2 s-4)$ are $-8(- s+3 s-4)$ , $(-2 s-4) \cdot-8$ , and $16 s+32$ .

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QuestionChoose the equivalent expressions for −8(−2s−4)-8(-2 s-4)−8(−2s−4). Options include: 1. −8(−5s+3s−4)-8(-5 s+3 s-4)−8(−5s+3s−4) 2. −8(−8s+6s−4)-8(-8 s+6 s-4)−8(−8s+6s−4) 3. (−2s−4)⋅−8(-2 s-4) \cdot-8(−2s−4)⋅−8 4. 16s+3216 s+3216s+32

Studdy Solution

STEP 1

Assumptions1. The expressions are equivalent if they simplify to the same result. . The distributive property of multiplication over addition/subtraction is valid, which states that for all real numbers a, b, and c a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

First, let's simplify the given expression −8(−2s−4)-8(-2 s-4)−8(−2s−4) using the distributive property.−8(−2s−4)=−8⋅−2s+−8⋅−4-8(-2 s-4) = -8 \cdot -2s + -8 \cdot -4−8(−2s−4)=−8⋅−2s+−8⋅−4

STEP 3

Perform the multiplication.−8⋅−2s+−8⋅−=16s+32-8 \cdot -2s + -8 \cdot - =16s +32−8⋅−2s+−8⋅−=16s+32

STEP 4

Now, let's simplify the first candidate expression −8(−s+3s−4)-8(- s+3 s-4)−8(−s+3s−4).−8(−s+3s−4)=−8⋅−2s+−8⋅−4-8(- s+3 s-4) = -8 \cdot -2s + -8 \cdot -4−8(−s+3s−4)=−8⋅−2s+−8⋅−4

STEP 5

Perform the multiplication.−8⋅−2s+−8⋅−4=16s+32-8 \cdot -2s + -8 \cdot -4 =16s +32−8⋅−2s+−8⋅−4=16s+32

STEP 6

The first candidate expression is equivalent to the given expression.

STEP 7

Now, let's simplify the second candidate expression −(−s+6s−4)-(- s+6 s-4)−(−s+6s−4).−(−s+6s−4)=−⋅−2s+−⋅−4-(- s+6 s-4) = - \cdot -2s + - \cdot -4−(−s+6s−4)=−⋅−2s+−⋅−4

STEP 8

Perform the multiplication.−8⋅−2s+−8⋅−4=16s+32-8 \cdot -2s + -8 \cdot -4 =16s +32−8⋅−2s+−8⋅−4=16s+32

STEP 9

The second candidate expression is not equivalent to the given expression.

STEP 10

Now, let's simplify the third candidate expression (−2s−4)⋅−8(-2 s-4) \cdot-8(−2s−4)⋅−8.(−2s−4)⋅−8=−8⋅−2s+−8⋅−4(-2 s-4) \cdot-8 = -8 \cdot -2s + -8 \cdot -4(−2s−4)⋅−8=−8⋅−2s+−8⋅−4

STEP 11

Perform the multiplication.−8⋅−s+−8⋅−4=16s+32-8 \cdot -s + -8 \cdot -4 =16s +32−8⋅−s+−8⋅−4=16s+32

STEP 12

The third candidate expression is equivalent to the given expression.

STEP 13

Now, let's compare the fourth candidate expression 16s+3216 s+3216s+32 to the simplified given expression.16s+32=16s+3216 s+32 =16s +3216s+32=16s+32

STEP 14

The fourth candidate expression is equivalent to the given expression.The expressions equivalent to −8(−2s−4)-8(-2 s-4)−8(−2s−4) are −8(−s+3s−4)-8(- s+3 s-4)−8(−s+3s−4), (−2s−4)⋅−8(-2 s-4) \cdot-8(−2s−4)⋅−8, and 16s+3216 s+3216s+32.

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QuestionChoose the equivalent expressions for $-8(-2 s-4)$ . Options include:
1. $-8(-5 s+3 s-4)$
2. $-8(-8 s+6 s-4)$
3. $(-2 s-4) \cdot-8$
4. $16 s+32$

First, let's simplify the given expression $-8(-2 s-4)$ using the distributive property.
$-8(-2 s-4) = -8 \cdot -2s + -8 \cdot -4$

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot - =16s +32$

Now, let's simplify the first candidate expression $-8(- s+3 s-4)$ .
$-8(- s+3 s-4) = -8 \cdot -2s + -8 \cdot -4$

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

Now, let's simplify the second candidate expression $-(- s+6 s-4)$ .
$-(- s+6 s-4) = - \cdot -2s + - \cdot -4$

Perform the multiplication.
$-8 \cdot -2s + -8 \cdot -4 =16s +32$

Now, let's simplify the third candidate expression $(-2 s-4) \cdot-8$ .
$(-2 s-4) \cdot-8 = -8 \cdot -2s + -8 \cdot -4$

Perform the multiplication.
$-8 \cdot -s + -8 \cdot -4 =16s +32$

Now, let's compare the fourth candidate expression $16 s+32$ to the simplified given expression.
$16 s+32 =16s +32$

The fourth candidate expression is equivalent to the given expression.
The expressions equivalent to $-8(-2 s-4)$ are $-8(- s+3 s-4)$ , $(-2 s-4) \cdot-8$ , and $16 s+32$ .