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

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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

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.

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

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