Algebra laws??

Question

Why does the calculation change if you know / don't know the value of the symbols?

for example  3a(2d+bc)-4c

I get 6ad+3abc-4c.

BUT....If the values are given a=2 b=3 c=4 d=6

With these values I get a final answer of 44 using the above calculation which apparently is correct if you DONT know the values, however this is wrong since now we are given the values. The actual answer is:

128.

I don't understand why you multiply each part of the inside of the bracket with the outside of the bracket when you don't know any values which by my understanding, goes against BODMAS.
However, if you know the values, you calculate the problem using BODMAS.

But each way is correct if you don't know the value. This has confused me so that I now don't know when to do each type of multiplication.

Please help me

Answer 1

If the values given are:

 

a=2

b=3

c=4

d=6

 

6ad + 3abc - 4c.

 

6(2)(6) + 3(2)(3)(4) - 4(4)

72 + 72 - 16

144 - 16 = 128

 

3a(2d + bc) - 4c

 

3(3)[2(6) + 3(4)] - 4(4)

brackets first

3(3)[12 + 12] - 4(4)

3(3)[24] - 4(4)

multiplication

9(24) - 16

addition/subtraction

144 - 16 = 128

 

You get the same answer whether you distribute the numbers or not. It's a convenient method when working with unknown variables allowing you to get rid of the brackets so you can simplify or manipulate the equation.

 

Answer 2

 

you get the same answer whether you distribute or not

 

3a(2d+bc)-4c

(3*2)(2*6+3*4)-4*4

(6)(12+12)-16

6*24-16

144-16=128

 

6ad+3abc-4c

6*2*6+3*2*3*4-4*4

72+72-16

144-16=128

 

The outcomes are the same!!

 

remember that you do multiplication and division in order from left to right whichever occurs first and then you add and subtract in order from left to right whichever occurs first

Answer 3

The correct answer is 128.

 

You do whatever is in the brackets first....but inside of the brackets, you may have to use the order of operations to reduce the expression in the brackets to a single number before proceeding with the rest of the problem.

 

So in your problem you would get....

 

3*2*(2*6 + 3*4) -4*4 ......you must evaluate the bracketed expression first to get 24.

3*2*24 - 4*4

144-16

128.

 

Hope this helped.