1. Factorise. \( \begin{array}{ll}\text { a) } a^{3}+b^{3} & \text { b) } a^{3}-b^{3} \\ \text { c) } a^{3}-27 b^{3} & \text { d) } 8 a^{3}+b^{3}(-1 \\ \text { e) } 125 x^{3}-64 y^{3} & \text { f) } 27 x^{3}+64 y^{3}< \\ \text { g) } 8 r^{3}-27 & \text { h) } x^{3}+1000 \\ & \text { i) } 125+8 a^{3}\end{array} \)

The factorization of cubes is a delightful mathematical trick. For \(a^3 + b^3\), it can be factored as \((a + b)(a^2 - ab + b^2)\). Meanwhile, \(a^3 - b^3\) goes like \((a - b)(a^2 + ab + b^2)\). These formulas can transform what looks like a complicated expression into a neat product of polynomials in the blink of an eye! Now, let's sprinkle in some real-world application! Factoring is not just a classroom exercise; it actually has its uses in various fields such as engineering, physics, and computer science. For example, simplifying polynomial expressions through factoring can help optimize algorithms or solve real-life problems involving curves and areas. So next time you factor a polynomial, think of it as untangling a knot that could lead to clearer solutions in practical scenarios!