Writing numbers as a product of primes, HCF & LCM, using BIDMAS, simplifying indices using index rules, show an expression as a power of one number, forming equations from a writte... Writing numbers as a product of primes, HCF & LCM, using BIDMAS, simplifying indices using index rules, show an expression as a power of one number, forming equations from a written problem, solving linear equations, simplifying expressions, substitution, factorising. Read more

Steps to Solve

1. Identify the Mathematical Concepts Review the list of concepts provided, such as "HCF & LCM," "BIDMAS," and "solving linear equations."

2. Understand Each Topic Break down each concept to understand its structure and rules. For example:

   • HCF & LCM: Highest Common Factor and Lowest Common Multiple.
   • BIDMAS: An acronym for Brackets, Indices, Division and Multiplication, Addition and Subtraction, indicating the order of operations.

3. Practice Writing Numbers as a Product of Primes For instance, to write 30 as a product of primes, factor it down:

   • (30 = 2 \times 3 \times 5)

4. Using BIDMAS for Complex Expressions Evaluate an expression like (3 + 2 \times (4 - 1)^2):

   • Brackets first: (4 - 1 = 3)
   • Indices: (3^2 = 9)
   • Division and Multiplication: (2 \times 9 = 18)
   • Finally, Addition: (3 + 18 = 21)

5. Simplifying Indices Apply index rules, such as (a^m \times a^n = a^{m+n}).

   • For example, simplify (x^2 \times x^3 = x^{2+3} = x^5).

6. Expressing as a Power of One Number For instance, express 64 as a power of 2:

   • (64 = 2^6)

7. Forming Equations from a Written Problem Translate a sentence like "Five more than twice a number is 15" into an equation:

   • Let (x) be the number: (2x + 5 = 15).

8. Solving Linear Equations Continuing from the last step, solve for (x):

   • (2x + 5 = 15)
   • Subtract 5: (2x = 10)
   • Divide by 2: (x = 5).

9. Simplifying Expressions Combine like terms, e.g., simplify (2x + 3x - 5 = 5x - 5).

10. Substitution If (x = 3), substitute into (2x + 1):

    • (2(3) + 1 = 6 + 1 = 7).

11. Factorising Rewrite (x^2 - 5x + 6) as ((x - 2)(x - 3)).