Working with formulas > Rewriting formulas
1234Rewriting formulas

Theory

Formulas like 2 l + 2 b = 60 and b = 30 l describe the same relatonship, they are equivalent. You can reduce (or rewrite ) the formula 2 l + 2 b = 60 :

2 l + 2 b = 60
both sides / 2
l + b = 30
both sides l
b = 30 l

b has now been expressed in l . The new formula contains fewer symbols and looks neater.
When rewriting formulas you use the following principles:

  • you may add or subtract the same from both sides of an equals sign;
    you may divide or multiply with the same number on both sides of an equals sign (except for multiplying or dividing by 0 );

  • removing brackets:
    a ( x + y ) = a x + a y
    and
    ( a + b ) ( c + d ) = a c + a d + b c + b d

  • factorizing:
    a x + a y = a ( x + y )
    and
    x 2 + p x + q = ( x + a ) ( x + b ) with a + b = p and a b = q

  • adding/subtracting/multiplying and dividing fractions:
    a b ± c d = a d b d ± b c b d = a d ± b c b d
    and
    a b c d = a c b d
    and
    a b / c d = a d b d / b c b d = a d b c
    if
    b 0 , c 0 (only when dividing) and d 0

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