[Math] Boolean simplification, 5 variables

Question

I'm currently learning for my maths exam, and in the part about boolean algebra I came across an exercise that I can't seem to solve. I probably only need the first few steps to get started.

$$ (xyz + uv)(x+\overline{y}+\overline{z}+uv) $$

Usually, if I get into trouble, I can fall back to a truth table or VK-diagram, but that's just too much work for 5 variables.

Thanks in advance!

Answer 1

Multiply the terms in the two brackets. You get: $$ xyz + 0 + 0 + xyzuv + xuv + \overline{y}uv + \overline{z}uv + uv$$ $$ xyz(1+uv) + uv(1+x+\overline{y}+\overline{z})$$ $$ xyz + uv $$

NOTE:

$1 + x = 1$

$1.x = x$

$x.x = x$

$x.\overline{x} = 0$