Expanding multiplies out brackets: every term in one factor times every term in the other, then like terms combined. (x + 1)³ expands to x³ + 3x² + 3x + 1 — the coefficients are a row of Pascal's triangle.
Isibonelo esisebenza: expand (x+1)^3
Symbols used here
Inequalities that allow equality; < and > exclude it.
Both signs at once: x = 3 ± 2 means 5 and 1.
The two sides are different.
The non-negative number whose square (n-th power) is x.
Distance from zero: |−3| = 3. For a complex number, distance from the origin.
i² = −1.
The exponent b must be raised to for x; ln uses base e.
Naturals, integers, rationals, reals, complex numbers.
How to: Expanding
- Start from the expression.
- Distribute (multiply out) the products.
Questions people ask
What does it mean to solve an equation?
To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.
Why do I sometimes get two answers?
A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.
How do I know whether to factor or use the quadratic formula?
Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.
Zama wena
Okuningi Algebra
Linear equationsQuadratic equationsSystems of equationsInequalitiesFactoringSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value