Algebra tiles to prove that 4 + 8x and 4 (2x+1)

Not sure what algebra tiles are

not sure how to absolutely prove

I can prove it works at least most of the time by subsitute ing number for x

remember that 0,1,2 have special properties and are not very good for subsituting so

try 4

4+8 (4) = 4 (2 (4) + 1)

true or false?

4+8 (4) = 4 (2 (4) + 1)

multipily

4+32=4 (8+1)

36=4 (9)

36=36

this is treu at least for the number 4

another way is to believe in the distributive property where

a (b+c) = ab+ac so then

4 (2x+1) = 4 (2x) + 4 (1) = 8x+4=4+8x

4 + 8x

Now, see if the simplified form of 4 (2x + 1) is equal to that.

4*2x = 8x

4*1 = 4

4 + 8x = 4 + 8x Correct