# Thread: Help with binomial expansions

1. ## Help with binomial expansions

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

2. Using a computer will be quite quick.

Its not a tricky one though, have you seen the F.O.I.L method?

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

FOIL will be quickest but you can also use the distributive property

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

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.