Working with formulas > Rewriting formulas
1234Rewriting formulas

## Theory

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

 $2l+2b$ $=$ $60$ 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:
$a\cdot \left(x+y\right)=a\cdot x+a\cdot y$
and
$\left(a+b\right)\cdot \left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

• factorizing:
$a\cdot x+a\cdot y=a\cdot \left(x+y\right)$
and
${x}^{2}+p\cdot x+q=\left(x+a\right)\cdot \left(x+b\right)$ with $a+b=p$ and $a\cdot b=q$

$\frac{a}{b}±\frac{c}{d}=\frac{a\cdot d}{b\cdot d}±\frac{b\cdot c}{b\cdot d}=\frac{a\cdot d±b\cdot c}{b\cdot d}$
$\frac{a}{b}\cdot \frac{c}{d}=\frac{a\cdot c}{b\cdot d}$
$\frac{a}{b}/\frac{c}{d}=\frac{a\cdot d}{b\cdot d}/\frac{b\cdot c}{b\cdot d}=\frac{a\cdot d}{b\cdot c}$
$b\ne 0$, $c\ne 0$(only when dividing) and $d\ne 0$