Substituting into a Formula

A formula is an expression with letters standing in for numbers you'll fill in later. $A = \ell w$ waits for a length and a width; $c^2 = a^2 + b^2$ waits for two legs. Substituting just means replacing each letter with its value.

The one place it goes wrong is signs. When a variable is negative, wrap it in parentheses as you substitute — $x = -4$ becomes $(-4)$, not a loose $-4$. That keeps $\,3x\,$ reading as $3 \times (-4)$ and $\,x^2\,$ reading as $(-4)^2 = 16$, not $-16$. Substitute with parentheses, then evaluate by the order of operations.

A plain expression. Evaluate $3x + 2$ when $x = 5$:

$3x + 2 = 3(5) + 2 = 15 + 2 = 17$

A real formula. The perimeter of a rectangle is $P = 2(\ell + w)$. With $\ell = 7$ and $w = 3$, do the parentheses first:

$P = 2(7 + 3) = 2(10) = 20$

Mind the negatives. Evaluate $x^2 + 1$ when $x = -5$. The parentheses are what save you:

$(-5)^2 + 1 = 25 + 1 = 26$

Without them, $-5^2$ would read as $-(5^2) = -25$ — a classic, avoidable slip.

Substitute with parentheses, then evaluate. A negative value is where most mistakes hide — predict before you check.