1. The problem asks to factorise the given expressions. 2. Factorisation means expressing an expression as a product of its factors. 3. For example, for the expression $3x - 12$, we look for the greatest common factor (GCF) of the terms. 4. The GCF of $3x$ and $12$ is $3$, so we factor out $3$: $$3x - 12 = 3(x - 4)$$ 5. Similarly, for $6y + 30$, the GCF is $6$: $$6y + 30 = 6(y + 5)$$ 6. For $5x^2 - 5x$, the GCF is $5x$: $$5x^2 - 5x = 5x(x - 1)$$ 7. For $-x^2y - 4x^2y^2$, the GCF is $-x^2y$: $$-x^2y - 4x^2y^2 = -x^2y(1 + 4y)$$ 8. Next, evaluate the expression $-2a^2$ by substituting a value for $a$ if given, or leave as is if no value is provided. Since no value for $a$ is given, the expression remains $-2a^2$. Final answers: - $3x - 12 = 3(x - 4)$ - $6y + 30 = 6(y + 5)$ - $5x^2 - 5x = 5x(x - 1)$ - $-x^2y - 4x^2y^2 = -x^2y(1 + 4y)$ - $-2a^2$ remains as is without a value for $a$.