Your first one ONLY.  I'll answer the others when I get time.

ax + bx + ay + by

Write it this way:

(ax + bx) + (ay + by)

Factor x out of the first parentheses

x(a + b) + (ay + by)

Factor y out of the second parentheses

x(a + b) + y(a + b)

Now I will color the (a + b)'s red:

x(a + b) + y(a + b)

Note that the red parentheses (a + b) is a 

factor of both those terms x(a + b) and y(a + b).

Therefore you can take out the "red" factor, you write

this

(a + b)( 

When you take (a + b) out of x(a + b), 

you get " x ", so put " x " next to the parenthesis

(a + b)(x

When you take (a + b) out of y(a + b), you get " y ", so put

" + y) " next to the x

(a + b)(x + y)

That's it!

Edwin





 

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