Hello, lsosa02!
How about using parentheses and spaces?
It's really difficult to
guess what you meant . . .
Factor: \(\displaystyle acx^{m+n}\,+\,adx^n\,+\,bcx^m\,+\,bd\)
The directions say to factor this into two groups and assume that a,b,c and dare constants.
Then it says to varify the factorization by multipliying.
Factor the first two terms: \(\displaystyle \,acx^{m+n}\,+\,adx^n\)
They have a common factor: \(\displaystyle \,ax^n\)
Factor it out: \(\displaystyle \,ax^n(cx^m\,+\,d)\)
Factor the last two terms: \(\displaystyle \,bcx^m\,+\,bd\)
They have a common factor: \(\displaystyle \,b\)
Factor it out: \(\displaystyle \,b(cx^m\,+\,d)\)
We have: \(\displaystyle \,ax^n(\underbrace{cx^m\,+\,d})\,+\,b(\underbrace{cx^m\,+\,d})\)
. . . . . . . . Do you see the common factor?
Factor it out: \(\displaystyle \
cx^m\,+\,d)\,(ax^n\,+\,b)\;\;\)
. . . There!
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Check
Multiply it out ("FOIL") . . .
We have: \(\displaystyle \,(cx^m\,+\,d)(ax^n\,+\,b)\)
\(\displaystyle \;\;\;=\;(cx^m)(ax^n)\,+\,(cx^m)(b)\,+\,(d)(ax^n)\,+\,(d)(b)\)
\(\displaystyle \;\;\;=\;acx^{m+n}\,+\,bcx^m\,+\,adx^n\,+\,bd\;\;\)
. . . check!