# Help with binomial expansions

• 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
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".

\$\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.