Writing expressions in the form of....

Question

Please help, I am so lost! The question states:

Use properties of real numbers to write the expression (5a)(10b+7c−3d) in the form of K⋅ab+M⋅ac+N⋅ad

Then, I must give three answers:

The number K=___

The number M=___

The number N=___

Answer 1

Hi Amber! So the question is asking what K, M, and N equal in terms of real numbers when the equation is in the form shown (Kab+Mac+Nad). We have this equation:

 

(5a)(10b+7c-3d)

 

And we want to get #ab+#ac+#ad. To do this, all we have to do is multiply the 5a by the other part of the expression. The 5a multiplies by each part of what is within the parentheses, so you get:

 

5a*10b + 5a*7c + 5a*-3d

 

50ab + 35ac + -15ad

 

Thus:
K=50

M=35

N=-15

 

If you would like more explanation or are interested in online tutoring, let me know and I would love to help out!

Answer 2

Let's apply the Distributive Property to the original expression....

 

(5a)(10b+7c-3d) = 50ab+35ac-15ad...distribute the term "5a" by multiplying

                                                                 it to each term inside the parentheses

   

Now take a look at the revised expression.  Doesn't it resemble the form 

"K•ab+M•ac+N•ad" as asked for in the question?

 

"K, M, and N" are the numerical coefficients of the terms "ab, ac, and ad".  

Remember to carry the sign (+ or -) with each coefficient.