Lesson goal: Simplify an algebraic expression
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In algebra,
simplifying an expression means writing it in the most compact and efficient form possible by:
- Multiplying out grouped terms and parenthesis
- Combining like terms (adding together terms with the same variable powers)
- Canceling opposite quantities
For instance, consider the expression $(x + 1)(x - 1) + 1$. The product $(x + 1)(x - 1)$ expands to $x^2 - 1$. Adding $1$ yields:
$$(x^2 - 1) + 1 = x^2$$
The
algebra("...") function simplifies complicated expressions down to their canonical polynomial form.
algebra("(x+1)*(x-1) + 1")algebra("(x+2)*(x+3) - 5*x - 6")
Move the mouse over a dotted box for more information.
The computer collects all like terms and simplifies everything down to irreducible polynomial forms.
Now you try.
Try simplifying (x + 4)*(x - 4) - x^2 and see what is left over.
Type your code here:
Notice how (x + 1) * (x - 1) produces $x^2 - 1$, and adding $1$ cancels the constant, leaving simply $x^2$.