Question

Are -1/3(-3m+6-12+15m) and 2(1-2m) equivalent expression?

Answer 1

Answer: -2and^2*(2m-1)^2

Step-by-step explanation: Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "d2" was replaced by "d^2".

STEP

1

:

1

Simplify —

3

Equation at the end of step

1

:

1

((((—•(12m-6))•a)•n)•d2)•(1-2m)

3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

12m - 6 = 6 • (2m - 1)

Equation at the end of step

3

:

(((2•(2m-1)•a)•n)•d2)•(1-2m)

STEP

4

:

Equation at the end of step 4

((2a • (2m - 1) • n) • d2) • (1 - 2m)

STEP

5

:

Equation at the end of step 5

(2an • (2m - 1) • d2) • (1 - 2m)

STEP

6

:

Equation at the end of step 6

2and2 • (2m - 1) • (1 - 2m)

STEP

7

:

7.1 Rewrite (1-2m) as (-1) • (2m-1)

Multiplying Exponential Expressions:

7.2 Multiply (2m-1) by (2m-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2m-1) and the exponents are :

1 , as (2m-1) is the same number as (2m-1)1

and 1 , as (2m-1) is the same number as (2m-1)1

The product is therefore, (2m-1)(1+1) = (2m-1)2

Final result :

-2and2 • (2m - 1)2

Answer 2

Yes, -1/3(-3m+6-12+15m) and 2(1-2m) are equivalent expressions. When simplified, both expressions can be written as -5m+4. This can be verified by substituting different values for m in both expressions and then simplifying the expressions. By doing so, the same result of -5m+4 will be obtained for both expressions indicating that they are equivalent

Explanation: