# Maths

### Quadratic Equations

A quadratic equation is one of the standard forms for equations in algebra, a quadratic equation in standard form looks like this:

#### ax^{2} + bx + c = 0

the name for quadratic equations comes from quad, meaning squared as the variable is squared. Sometimes elements of quadratic equations are not shown, for example, if a = 1 it is not shown and if c = 0 it is not shown either.

sometimes quadratic equations can be disquised and not look like they do in standard form, for example x^{2} = 3x - 1 in standard form it look like this, x^{2} - 3x + 1 = 0, when you have a hidden quadratic equation like this, you have to move all the terms to left hand side, and remember that postives become negatives and vice versa when moved the another side of the equals.

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### Simplifying Expressions

Before Using and evaluating an equation, you will first want to simplify it, this will make the calculations much easier. The 4 Basic steps to simplify an expression are:

1. remove parentheses by multiplying factors

2. use exponent rules to remove parentheses from terms with exponents

3. combine like terms

4. combine constants

When simplifying an expression, you can often use the distributive property to clear out parentheses in an equation by multiplying the factors by the terms inside the parentheses. You can also remove parentheses from a term with exponents thanks to several exponent rules, when a term with an exponent in it also has an exponent, you can multiply the exponents, so (x^2)^2 becomes x^4. The next part of simplifying is finding like terms and combining them, for example terms like 5x and 15x are like terms, they have the same kind of number interacting with the same variable, or raised to the same power. Next you can look for any constants that can be combined. And finally, equations are written in a specific order, Starting with the terms with largest exponents, and slowly moving down to the constants, equations can be re-arranged like this because of the cumulative property of addition. Using these steps is all that is needed to turn an equation such as "5(2+x)+3(5x+4)-(x^2)^2" into "=-x^4+20x+22"