Multiply the algebraic expression using a Special Product Formula and simplify. \[ (2 x+5)^{2} \] 25

To multiply the algebraic expression \((2x + 5)^2\), you can use the Special Product Formula for the square of a binomial, which states that \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = 2x\) and \(b = 5\). So, applying the formula: \[ (2x + 5)^2 = (2x)^2 + 2(2x)(5) + (5)^2 = 4x^2 + 20x + 25 \] Now you've successfully multiplied and simplified the expression! In mathematics, special product formulas are a blast because they save you time and energy in calculations! Mastering these can help you solve problems faster, especially in algebra where such expressions pop up frequently. Embrace these shortcuts, and they’ll turn the complexities of math into a walk in the park. Another fun fact is that these formulas are foundational in many areas of science and engineering. For instance, they can simplify polynomial equations in physics, chemistry, or even economics, enabling professionals to model complex scenarios or perform calculations with ease. Understanding and applying these special products can truly enhance your problem-solving toolkit!