Is there a quick way to expand: (3x + 5)(x - 7)?

(Crying)

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- Dec 2nd 2010, 04:58 PMAJDHelp with binomial expansions
Is there a quick way to expand: (3x + 5)(x - 7)?

(Crying) - Dec 3rd 2010, 11:58 AMpickslides
Using a computer will be quite quick.

Its not a tricky one though, have you seen the F.O.I.L method? - Dec 3rd 2010, 12:03 PMe^(i*pi)
- Dec 3rd 2010, 12:33 PMArchie Meade
This is a good example where you may say "and" instead of "plus".

$\displaystyle (2+3)(1+5)=5(6)=30$

We may also write

$\displaystyle (2+3)(1+5)=2(1+5)$ and $\displaystyle 3(1+5)$ or $\displaystyle 1(2+3)$ and $\displaystyle 5(2+3)$

which is

$\displaystyle 2(1)$ and $\displaystyle 2(5)$ and $\displaystyle 3(1)$ and $\displaystyle 3(5)$

$\displaystyle 2+10+3+15=30$

The whole is the sum of the parts

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$\displaystyle (3x+5)(x-7)=3x(x-7)+5(x-7)=3x(x)+3x(-7)+5(x)+5(-7)$

which is the 3x multiplied by both in the 2nd brackets and 5 by both in the 2nd brackets.