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QuestionIdentify equivalent expressions to 2(b+3c)2(b+3 c) from the following options: 3(b+2c)3(b+2 c), (b+3c)+(b+3c)(b+3 c)+(b+3 c), 2(b)+2(3c)2(b)+2(3 c).

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions equivalent to (b+3c)(b+3 c). The expressions to be considered are 3(b+c)3(b+ c), (b+3c)+(b+3c)(b+3 c)+(b+3 c), and (b)+(3c)(b)+(3 c)

STEP 2

First, let's simplify the given expression 2(b+c)2(b+ c) using the distributive property of multiplication over addition.
2(b+c)=2b+2(c)2(b+ c) =2b +2(c)

STEP 3

Further simplify the expression.
2(b+3c)=2b+6c2(b+3 c) =2b +6c

STEP 4

Now, let's simplify the first expression to be considered, 3(b+2c)3(b+2 c), using the distributive property of multiplication over addition.
3(b+2c)=3b+3(2c)3(b+2 c) =3b +3(2c)

STEP 5

Further simplify the expression.
3(b+2c)=3b+c3(b+2 c) =3b +c

STEP 6

Comparing the simplified expressions 2(b+3c)=2b+6c2(b+3 c) =2b +6c and 3(b+2c)=3b+6c3(b+2 c) =3b +6c, we can see that they are not equivalent because the coefficients of bb are not the same.

STEP 7

Next, let's simplify the second expression to be considered, (b+3c)+(b+3c)(b+3 c)+(b+3 c).
This is simply the sum of two identical expressions, so we can add the like terms together.

STEP 8

implify the expression.
(b+3c)+(b+3c)=2b+6c(b+3 c)+(b+3 c) =2b +6c

STEP 9

Comparing the simplified expressions 2(b+3c)=2b+6c2(b+3 c) =2b +6c and (b+3c)+(b+3c)=2b+6c(b+3 c)+(b+3 c) =2b +6c, we can see that they are equivalent.

STEP 10

Finally, let's simplify the third expression to be considered, 2(b)+2(3c)2(b)+2(3 c).
This is simply the sum of two multiplied expressions, so we can add the like terms together.

STEP 11

implify the expression.
(b)+(3c)=b+6c(b)+(3 c) =b +6c

STEP 12

Comparing the simplified expressions 2(b+c)=2b+6c2(b+ c) =2b +6c and 2(b)+2(c)=2b+6c2(b)+2( c) =2b +6c, we can see that they are equivalent.
The expressions equivalent to 2(b+c)2(b+ c) are (b+c)+(b+c)(b+ c)+(b+ c) and 2(b)+2(c)2(b)+2( c).

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