Welcome to Algebra Revision Quiz (F) P4, which will help you brush up on your algebra skills and continues from Part 1, 2 and 3 - which can be found here:

Algebra is an essential topic in GCSE mathematics that involves using letters, symbols, and variables to represent numbers and quantities. It provides a powerful tool for solving problems and simplifying expressions that involve arithmetic operations such as addition, subtraction, multiplication, and division. In this explanation, we will discuss the laws of indices, expanding expressions, solving equations, and using algebra in problem-solving questions.

## Laws of Indices

The indices' laws help simplify expressions involving powers and exponents in algebra. These laws include the product law, the quotient law, and the power law. For example:

Product law: am × an = a(m+n)

If, a = 2, m = 3, and n = 4, then 23 × 24 = 2(3+4) = 27 = 128.

Quotient law: am ÷ an = a(m-n)

If, a = 2, m = 5, and n = 2, then 25 ÷ 22 = 2(5-2) = 23 = 8.

Power law: (am)n = a(mn)

If a = 3, m = 2, and n = 3,

Then, (32)3 = 3(2×3) = 36 = 729.

## Expanding expressions

Expanding an expression involves multiplying each term inside the bracket by the number outside the bracket. For example:

3(x + 4) = 3x + 12

If x = 2,

Then, 3(2+4) = 3×2 + 12 = 18.

## Solving equations

An equation is a statement showing two expressions are equal, and solving an equation means finding the variable's value that makes the equation true. To solve an equation, we need to keep it balanced by doing the same thing to both sides of the equation. For example:

2x + 5 = 11

Subtracting 5 from both sides: 2x = 6

Dividing by 2: x = 3