7actorise \( 125 x^{3}+27 \)

To factor \( 125x^{3} + 27 \), we recognize that this expression is a sum of cubes. We can rewrite it as \( (5x)^{3} + 3^{3} \). To factor a sum of cubes, we can use the formula \( a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2}) \). Here, \( a = 5x \) and \( b = 3 \). Applying the formula yields: \[ (5x + 3)((5x)^{2} - (5x)(3) + (3)^{2}) = (5x + 3)(25x^{2} - 15x + 9) \] And there we have it: \( 125x^{3} + 27 = (5x + 3)(25x^{2} - 15x + 9) \)! Understanding this can come in handy! Just think of all the times you might want to apply this in algebra, like simplifying complex equations or solving polynomial equations. It’s like knowing a magic trick that can really impress your friends during math homework sessions! If you're curious about factorizations or algebra concepts, there are plenty of excellent resources such as "Algebra" by Israel M. Gelfand and Alexander Shen, or online platforms like Khan Academy that break concepts down into bite-sized pieces. They help transform algebra from a scary monster to a friendly puzzle!