QuestionFind expressions equivalent to $3(5 f+7)+7 f$ . Options include $5(7 f+3)+7 f$ , $7(3 f+5)+7 f$ , $3(4 f+f+7)+7 f$ , and $12 f+21$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3(5f+7)+7f$ . . We are asked to find the expressions that are equivalent to the given expression.

STEP 2

First, let's simplify the given expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds.
$(5f+7)+7f =15f +21 +7f$

STEP 3

Combine like terms.
$15f +21 +7f =22f +21$

STEP 4

Now, let's apply the same steps to each of the provided expressions to see if they simplify to the same result.
For the first expression, $(7f+3)+7f$ , apply the distributive property $(7f+3)+7f =35f +15 +7f$

STEP 5

Combine like terms.
$35f +15 +7f =42f +15$

STEP 6

For the second expression, $(3f+5)+f$ , apply the distributive property $(3f+5)+f =21f +35 +f$

STEP 7

Combine like terms.
$21f +35 +7f =28f +35$

STEP 8

For the third expression, $3(4f+f+7)+7f$ , apply the distributive property $3(4f+f+7)+7f =12f +3f +21 +7f$

STEP 9

Combine like terms.
$12f +3f +21 +7f =22f +21$

STEP 10

The fourth expression, $12f+21$ , is already simplified.

STEP 11

Now, compare each of the simplified expressions with the simplified form of the given expression, $22f +21$ .
The first expression, $42f +15$ , is not equivalent to $22f +21$ .
The second expression, $28f +35$ , is not equivalent to $22f +21$ .
The third expression, $22f +21$ , is equivalent to $22f +21$ .
The fourth expression, $f +21$ , is not equivalent to $22f +21$ .
So, the expressions equivalent to $3(5f+7)+7f$ are $3(4f+f+7)+7f$

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QuestionFind expressions equivalent to $3(5 f+7)+7 f$ . Options include $5(7 f+3)+7 f$ , $7(3 f+5)+7 f$ , $3(4 f+f+7)+7 f$ , and $12 f+21$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3(5f+7)+7f$ . . We are asked to find the expressions that are equivalent to the given expression.

STEP 2

First, let's simplify the given expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds.
$(5f+7)+7f =15f +21 +7f$

STEP 3

Combine like terms.
$15f +21 +7f =22f +21$

STEP 4

Now, let's apply the same steps to each of the provided expressions to see if they simplify to the same result.
For the first expression, $(7f+3)+7f$ , apply the distributive property $(7f+3)+7f =35f +15 +7f$

STEP 5

Combine like terms.
$35f +15 +7f =42f +15$

STEP 6

For the second expression, $(3f+5)+f$ , apply the distributive property $(3f+5)+f =21f +35 +f$

STEP 7

Combine like terms.
$21f +35 +7f =28f +35$

STEP 8

For the third expression, $3(4f+f+7)+7f$ , apply the distributive property $3(4f+f+7)+7f =12f +3f +21 +7f$

STEP 9

Combine like terms.
$12f +3f +21 +7f =22f +21$

STEP 10

The fourth expression, $12f+21$ , is already simplified.

STEP 11

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QuestionFind expressions equivalent to 3(5f+7)+7f3(5 f+7)+7 f3(5f+7)+7f. Options include 5(7f+3)+7f5(7 f+3)+7 f5(7f+3)+7f, 7(3f+5)+7f7(3 f+5)+7 f7(3f+5)+7f, 3(4f+f+7)+7f3(4 f+f+7)+7 f3(4f+f+7)+7f, and 12f+2112 f+2112f+21.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 3(5f+7)+7f3(5f+7)+7f3(5f+7)+7f. . We are asked to find the expressions that are equivalent to the given expression.

STEP 2

First, let's simplify the given expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds.(5f+7)+7f=15f+21+7f(5f+7)+7f =15f +21 +7f(5f+7)+7f=15f+21+7f

STEP 3

Combine like terms.15f+21+7f=22f+2115f +21 +7f =22f +2115f+21+7f=22f+21

STEP 4

Now, let's apply the same steps to each of the provided expressions to see if they simplify to the same result.For the first expression, (7f+3)+7f(7f+3)+7f(7f+3)+7f, apply the distributive property(7f+3)+7f=35f+15+7f(7f+3)+7f =35f +15 +7f(7f+3)+7f=35f+15+7f

STEP 5

Combine like terms.35f+15+7f=42f+1535f +15 +7f =42f +1535f+15+7f=42f+15

STEP 6

For the second expression, (3f+5)+f(3f+5)+f(3f+5)+f, apply the distributive property(3f+5)+f=21f+35+f(3f+5)+f =21f +35 +f(3f+5)+f=21f+35+f

STEP 7

Combine like terms.21f+35+7f=28f+3521f +35 +7f =28f +3521f+35+7f=28f+35

STEP 8

For the third expression, 3(4f+f+7)+7f3(4f+f+7)+7f3(4f+f+7)+7f, apply the distributive property3(4f+f+7)+7f=12f+3f+21+7f3(4f+f+7)+7f =12f +3f +21 +7f3(4f+f+7)+7f=12f+3f+21+7f

STEP 9

Combine like terms.12f+3f+21+7f=22f+2112f +3f +21 +7f =22f +2112f+3f+21+7f=22f+21

STEP 10

The fourth expression, 12f+2112f+2112f+21, is already simplified.

STEP 11

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QuestionFind expressions equivalent to $3(5 f+7)+7 f$ . Options include $5(7 f+3)+7 f$ , $7(3 f+5)+7 f$ , $3(4 f+f+7)+7 f$ , and $12 f+21$ .

Assumptions1. We are given the expression $3(5f+7)+7f$ . . We are asked to find the expressions that are equivalent to the given expression.

First, let's simplify the given expression by applying the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds.
$(5f+7)+7f =15f +21 +7f$

Combine like terms.
$15f +21 +7f =22f +21$

Now, let's apply the same steps to each of the provided expressions to see if they simplify to the same result.
For the first expression, $(7f+3)+7f$ , apply the distributive property $(7f+3)+7f =35f +15 +7f$

Combine like terms.
$35f +15 +7f =42f +15$

For the second expression, $(3f+5)+f$ , apply the distributive property $(3f+5)+f =21f +35 +f$

Combine like terms.
$21f +35 +7f =28f +35$

For the third expression, $3(4f+f+7)+7f$ , apply the distributive property $3(4f+f+7)+7f =12f +3f +21 +7f$

Combine like terms.
$12f +3f +21 +7f =22f +21$

The fourth expression, $12f+21$ , is already simplified.