actorise \( 4 x^{2}-y^{2} \)

To factor the expression \( 4x^{2} - y^{2} \), you can recognize it as a difference of squares. It's structured as \( (2x)^{2} - (y)^{2} \). Using the difference of squares formula \( a^{2} - b^{2} = (a - b)(a + b) \), we can factor it as follows: \( 4x^{2} - y^{2} = (2x - y)(2x + y) \). Now you have a beautifully factored form of the expression! For an extra sprinkle of fun: the concept of factoring has roots in ancient mathematics where it was used to solve problems involving areas and geometry. Imagine ancient mathematicians getting all excited digging into shapes and lengths, just like we are with our equations today! Dive into this world and see how math has always been a bridge between art and logic. And speaking of practical applications, factoring plays an essential role in fields like engineering and physics. Whether it’s simplifying algorithms in computer science or optimizing equations for a structural design, the ability to factor allows professionals to streamline complex calculations and make critical decisions more swiftly. Who knew those algebra classes had future-world-solving implications, right?