First question:

From the book... whomever wrote this doesn't know HOW to explain things.

Solve:

$\displaystyle p(m-n)-q(n-m)$

$\displaystyle p(m-n)-q(-1)(-n+m)$

From the second two terms, pull out a ‘-1’. You can double check that this is correct by distributing the “-1” back in.

$\displaystyle p(m-n)-q(-1)(m-n)$

Inside the parenthesis on the far right, rearrange terms.

$\displaystyle p(m-n)+q(m-n)$

Answer:Now, in the second group of terms, we have a “-1” times a “-1” which gives a “+1”.

$\displaystyle (m-n)(p+q)$

Can someone explain how the answer is obtained better? I'm fumbling on factoring with -1 on these types of equations.

-----------------------------------------

Second question:

Solve:

$\displaystyle 3x(c-3d)+6y(c-3d)$

Answer:

$\displaystyle 3(c-3d)(x+2y)$

If you apply the order of distribution it comes out to $\displaystyle 3c-9d...$

Why can't the answer be

$\displaystyle (c-3d)(x+2y)3$

or

$\displaystyle 3(x+2y)(c-3d)$

-----------------------------------------

Anyone have a better explanation? I'm starting to cram for a COMPASS test this coming Friday and still need to refresh my math skills from algebra, adv. algebra, geo, and trig.