# Help with binomial expansions

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

(Crying)
• Dec 3rd 2010, 11:58 AM
pickslides
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 PM
e^(i*pi)
Quote:

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

(Crying)

FOIL will be quickest but you can also use the distributive property
• Dec 3rd 2010, 12:33 PM
Archie Meade
Quote:

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

(Crying)

This is a good example where you may say "and" instead of "plus".

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

We may also write

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

which is

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

$2+10+3+15=30$

The whole is the sum of the parts

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

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