Final answer:
To factorise an expression, eliminate common terms, consider each factor while holding others constant, and apply rules for multiplying and dividing exponentials. Always check that your final simplified expression is correct.
Step-by-step explanation:
When asked to factorise an algebraic expression, you'll want to look for common factors and patterns that will help to simplify the expression. This often involves identifying greatest common factors or recognizing special products such as the difference of squares, perfect square trinomials, or sum/difference of cubes. Here are a few steps to consider when factorising:
- Eliminate terms wherever possible to simplify the algebra. This step is about reducing the expression by canceling out common factors.
- Consider the factors on the left-hand side of the equation one at a time, while holding the other factors constant.
- Multiplication of Exponentials: Multiply the digit terms in the usual way and add the exponents of the exponential terms.
- Division of Exponentials: Divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms.
Finally, always check your answers to make sure they are reasonable and correctly simplified. This might include substituting values back into the original equation to ensure the factorised form is equivalent.