Factorise fully D $$ 27 x^{3}-1 $$ 2) $$ 8 x^{3}+1 $$ 3 $$ x^{2}-5 x+6 $$ A $$ x^{2}-6 x-6 x-y^{2}+3 y $$ 5) $$ 2 a^{2}-a-15 $$

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Factor the expression by following steps:
- step0: Factor:
  $$2a^{2}-a-15$$
- step1: Rewrite the expression:
  $$2a^{2}+\left(5-6\right)a-15$$
- step2: Calculate:
  $$2a^{2}+5a-6a-15$$
- step3: Rewrite the expression:
  $$a\times 2a+a\times 5-3\times 2a-3\times 5$$
- step4: Factor the expression:
  $$a\left(2a+5\right)-3\left(2a+5\right)$$
- step5: Factor the expression:
  $$\left(a-3\right)\left(2a+5\right)$$
Factor the expression $$ x^{2}-5 x+6 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{2}-5x+6$$
- step1: Rewrite the expression:
  $$x^{2}+\left(-2-3\right)x+6$$
- step2: Calculate:
  $$x^{2}-2x-3x+6$$
- step3: Rewrite the expression:
  $$x\times x-x\times 2-3x+3\times 2$$
- step4: Factor the expression:
  $$x\left(x-2\right)-3\left(x-2\right)$$
- step5: Factor the expression:
  $$\left(x-3\right)\left(x-2\right)$$
Factor the expression $$ 8 x^{3}+1 $$.
Factor the expression by following steps:
- step0: Factor:
  $$8x^{3}+1$$
- step1: Rewrite the expression:
  $$\left(2x\right)^{3}+1^{3}$$
- step2: Factor the expression:
  $$\left(2x+1\right)\left(\left(2x\right)^{2}-2x\times 1+1^{2}\right)$$
- step3: Evaluate:
  $$\left(2x+1\right)\left(4x^{2}-2x+1\right)$$
Factor the expression $$ 27 x^{3}-1 $$.
Factor the expression by following steps:
- step0: Factor:
  $$27x^{3}-1$$
- step1: Rewrite the expression:
  $$\left(3x\right)^{3}-1^{3}$$
- step2: Factor the expression:
  $$\left(3x-1\right)\left(\left(3x\right)^{2}+3x\times 1+1^{2}\right)$$
- step3: Evaluate:
  $$\left(3x-1\right)\left(9x^{2}+3x+1\right)$$
Here are the fully factored forms of the given expressions:

1. **For $$ 27 x^{3}-1 $$**:
   $$
   27 x^{3}-1 = (3x-1)(9x^{2}+3x+1)
   $$

2. **For $$ 8 x^{3}+1 $$**:
   $$
   8 x^{3}+1 = (2x+1)(4x^{2}-2x+1)
   $$

3. **For $$ x^{2}-5 x+6 $$**:
   $$
   x^{2}-5 x+6 = (x-3)(x-2)
   $$

4. **For $$ x^{2}-6 x-6 x-y^{2}+3 y $$**:
   - This expression seems to have a mistake in the terms. It simplifies to $$ x^{2}-12x-y^{2}+3y $$. However, I couldn't find a result for this expression. Please check the expression for any errors.

5. **For $$ 2 a^{2}-a-15 $$**:
   $$
   2 a^{2}-a-15 = (a-3)(2a+5)
   $$

If you need further assistance or clarification on any of these, feel free to ask!
Here are the fully factored forms: 1. $$ 27x^3 - 1 = (3x - 1)(9x^2 + 3x + 1) $$ 2. $$ 8x^3 + 1 = (2x + 1)(4x^2 - 2x + 1) $$ 3. $$ x^2 - 5x + 6 = (x - 3)(x - 2) $$ 4. $$ x^2 - 12x - y^2 + 3y = $$ (Cannot factor as given) 5. $$ 2a^2 - a - 15 = (a - 3)(2a + 5) $$

Factorise fully D \( 27 x^{3}-1 \) 2) \( 8 x^{3}+1 \) 3 \( x^{2}-5 x+6 \) A \( x^{2}-6 x-6 x-y^{2}+3 y \) 5) \( 2 a^{2}-a-15 \)

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