Learn: Introduction to Algebra

Welcome!Today we'll learn the basics of Algebra. This is an important topic in mathematics that helps you solve problems using letters and symbols to represent numbers.Let's explore its key concepts step by step!

What is Algebra?Algebra is a branch of mathematics where we use letters or symbols to represent numbers and quantities in equations and expressions. It allows us to solve problems and understand relationships between numbers.For example, instead of writing '3 + 5 = 8,' in algebra we might write 'x + 5 = 8' and solve for x.

Key Algebra TermsLet's go over some important terms you'll need to know in algebra:Variable: A symbol (like x or y) that represents a number.Expression: A combination of numbers, variables, and operations (e.g., x + 2).Equation: A statement where two expressions are equal (e.g., x + 2 = 5).Coefficient: A number that multiplies a variable (e.g., in 3x, the coefficient is 3).

Solving EquationsTo solve an equation, we find the value of the variable that makes the equation true. For example, in the equation 'x + 3 = 7,' we need to find x.To solve, we subtract 3 from both sides: x = 7 − 3, so x = 4.

Expanding and SimplifyingSometimes, you'll need to expand expressions by multiplying terms. For example, expand 2(x + 3):Multiply 2 by x, then 2 by 3: 2(x + 3) = 2x + 6.You might also need to simplify expressions, which means combining like terms. For example, simplify 3x + 2x + 4: 3x + 2x = 5x, so the simplified expression is 5x + 4.

Factorising ExpressionsFactorising involves writing an expression as a product of its factors. For example, factorise 6x + 9:The highest common factor of 6 and 9 is 3, so we can write: 6x + 9 = 3(2x + 3).

Review Time!Great work! You've learned about variables, expressions, equations, expanding, simplifying, and factorising. Now let's test your understanding with a few questions.

Well Done!You've completed the lesson on Algebra basics. Keep practising to become confident with variables, expressions, equations, expanding, simplifying, and factorising!