how do you factorise?

for example putting 2x² + x - 3 into the form (2x + 3)(x - 1)

factorise
9x to the power of 4 - 64y to the power of 2

To factorise an expression, follow these steps:

1. Identify if there are any common factors. If there is a common factor among all the terms, factor it out.

2. Look for patterns that can be factored using special factorization formulas.
- For example, a² - b² factors as (a + b)(a - b).

3. If the expression has more than two terms, check if it can be factored by grouping. Look for pairs of terms that have common factors and factor them separately.

4. If the expression is a quadratic trinomial in the form ax² + bx + c, you can use the AC method or trial and error to find two binomials that multiply to give the trinomial.

Now let's factorise the expression 9x^4 - 64y^2:

Step 1: There are no common factors among the terms.

Step 2: Notice that the expression has the form a^2 - b^2, which can be factored as (a + b)(a - b). Rewrite the expression as (3x^2)^2 - (8y)^2.

Step 3: Apply the formula from step 2.
- (3x^2 + 8y)(3x^2 - 8y)

Therefore, 9x^4 - 64y^2 can be factorised as (3x^2 + 8y)(3x^2 - 8y).