what is the distributive property of -3(6-p)?what is the distributive property of -3(6-p)?

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lynn30k's profile pic

lynn30k | High School Teacher | (Level 1) Educator

Posted on

Distributive property applied to the expression  -3(6-p) means that because we are multilplying the quantity -3 by everything in the parenthesis, we can multiply them separately.

To do this, first multiply -3 by 6.  The quantity is 18, and because we have a positive times a negative number, the quantity is actually      -18.

Next, we multiply -3 by -p. Within the parenthesis, we can think of       6-p as the same thing as 6 + (-p)  For this term, we get positive 3p, as a neg. times a neg. gives a positive.

So the term can be rewritten as -18 + 3p

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The distributivity is a property of multiplication over addition.

For instance, the given example proves this property.

We'll multiply -3 by each term inside the brackets:

-3(6-p)

-3*6 = -18

-3*(-p) = 3p

Now, we'll add the results:

-3(6-p) = -18 + 3p

Since the terms are not alike and we cannot combine them furtermore, we'll consider the result as being the final result.

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

Distributive property, also called distributive law, refers to the fact that multiplying a number (say x) with sum of two numbers (say a and b) is equivalent of the sum of multiplication of the original number with each of the other two numbers.

Expresses as formula this means:

x*(a + b) = x*a + x*b

Applying this law to the given expression:

x = -3, a = 6 and b = - p

Therefore:

-3*(6 - p) = -3*6 - (-3)*(-p) = 18 + 3*p

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The distributive property of multiplication over addtion or subtraction is given by a* (b+c) = a*b+a*c. Or

a*(b-c) = a*b - a*c)

Here a = -3 , b = 6 and c = p.

So -3*{6 - p} = -3*6 - (-3)*p

-3{6 - p) = -18 +3p , as -(-p) =  p

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