use the distributive property to rewrite this expression. -5(b-4)

Question

use the distributive property to rewrite this expression. -5(b-4)

 

Answer 1

Tami,

 

Factoring is when we pull a common factor such as -5 out of an expression by dividing and then it might look like your problem here.  The reverse of that is when we use distributive property to multiply that same -5 by each item in the expression inside the parenthesis.

 

Looking in your parenthesis you have two terms, b and -4.  Think of it as adding b to -4.  So, -5*(b + -4).

So to use distributive property (you multiply), you take the -5 and multiply by b to get -5b and you then multiply that same -5 by -4 to get --20 which is +20.  Now your answer is those two terms, -5b + +20 or simply, -5b + 20.

 

(Now if you have already been factoring, you can factor out the -5 and get your original problem.  If not, you'll learn that later.)

 

Best, Kim

Answer 2

Hi Tami!  As you may be aware, the distributive property is a way to simplify an algebraic equation.  The expression that needs to be simplified comes in the form x ( y + z ) -- which is "x times the sum of y and z."  In your case, x = -5, y = b, and z = -4, so it's -5 times the sum of b and -4.

 

Using the distributive property, x ( y + z ) can be written as ( x * y ) + ( x * z ).  You can then use arithmetic to simplify the result.

 

For example, if x = -3, y = 2, and z = -4k, then the expression -3(2-4k) could be written as ( -3 * 2 ) + ( -3 * -4k ), and this can be simplified to (-6) + (12k), or -6 + 12k.

 

What equation, in the form (x*y)+(x*z), would you get by substituting the values from your expression into x, y, and z?  Next, how can you simplify the result?

Answer 3

-5(b-4)

 

-5b + 20 is the answer

 

Other examples of distributive problems:

 

2(x+y)

2x + 2y

 

 

9(3+2)

27 + 18

 

 

-8(x - y)

-8x + 8y  (notice that the two negative signs multiplied give you a positive result)

 

8(x - y)

8x - 8y

 

 

4x(2y - 9z)

8xy - 36xz