Algebra is a branch of mathematics that **uses letters, symbols, and numbers to represent and manipulate mathematical expressions and equations. **In GCSE Mathematics, algebra is an important tool for solving various mathematical problems, including word problems, equations, and inequalities.

**variables, usually represented by letters such as x, y, or z. Variables represent unknown values or quantities that vary in a given equation or expression.****For example, **consider the equation:

3x + 5 = 20

**In this equation, the variable "x" represents an unknown quantity we must solve.** By using algebraic techniques, we can rearrange the equation to isolate the variable on one side of the equation:

3x + 5 - 5 = 20 - 5

3x = 15

x = 5

Here, **we have solved for the value of "x" by using algebra to isolate it on one side of the equation.**

**A function is a relationship between two variables, usually represented by the letter "f(x)".****For example,** consider the function:

f(x) = 2x + 3

In this function, the **variable "x" represents the input, **and the expression** "2x + 3" represents the output.** To evaluate the function for a specific input value, **we substitute that value for "x" and simplify the expression.**

**For example,** to evaluate the function at "x = 4", we can substitute 4 for "x" and simplify the expression:

f(4) = 2(4) + 3

f(4) = 8 + 3

f(4) = 11

Here, **we have evaluated the function** at "x = 4" and obtained the corresponding output value of 11.

**is another important concept in algebra, and it**

**factorisation**

**involves breaking down an expression into simpler terms.**For example, consider the **quadratic equation:**

x^{2} + 5x + 6 = 0

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