MHB Use algebraic manipulation to prove the distributivity property

[shamieh]

Use algebraic manipulation to prove that x+yz=(x+y)(x+z) Note that this is
the distributive rule,

So I have:

(x + y)(x + z) = xx + xz + xy + zy
= x + xz + xy + zy
= x(1 + z + y) zy
=x * 1 + (z + y)(zy)
= x + ((zzy + yzz)
= x +y + z?

but i need x + yz... But I don't understand what is going on in the right side

 

[Deveno]

I don't understand what you are doing, either.

(x + y)(x + z) = (x + y)x + (x + y)z

= xx + yx + xz + yz = xx + xy + xz + yz (since xy = yx)

= x + xy + xz + yz (since xx = x)

= x(1 + y + z) + yz =...?