Use the distributive property to remove the parentheses. 8(x+2)

Question

Use the distributive property to remove the parentheses. Help?

Answer 1

The full proper name for the 'distributive property' is the distribution of multiplication over addition property

 

We know that the order of operations expects that 9(3 + 8) would add first b/c of the parentheses to give 9•11 = 99.

 

Note however that if we did 9•3 +9•8 yields 27 + 72 = 99.

 

The distributive property of multiplication over addition allows us to open the parentheses by 'the back door'. We cannot always compute the addition inside the parentheses.

 

So 8(x + 2) rewrites as 8x + 8•2 which is simplified to 8x + 16. We still cannot get computed result, but by opening the parentheses, we can do some further simplifications and combinations that would not have been available to us.

 

8(x + 2) + 7(x − 5) − 3(x − 4)

8x + 16 + 7x − 35 − 3x +12

 

8x + 7x − 3x + 16 − 35 + 12 by the commutative and associative properties of addition

 

12x − 7

 

The simple rewrite can facilitate the consolidation of 'like terms'.

Answer 2

a(b+c) = ab+ac

so 8(x+2) = 8x+16