O Exponenta and Polynomials Squaring a binomial: Univariate \( (7 y-3)^{2} \) Rewrite without parentheses and simplify. \( (7) \)

To square the binomial \( (7y - 3)^{2} \), you can use the formula \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = 7y \) and \( b = 3 \). Thus, we have: \[ (7y - 3)^{2} = (7y)^{2} - 2(7y)(3) + (3)^{2} = 49y^{2} - 42y + 9. \] Now you have a polynomial \( 49y^{2} - 42y + 9 \) that is simplified and no longer has parentheses. If you ever find yourself squaring a binomial, remember that the process can be visualized as expanding a rectangle: one side represents \( a \), the other \( b \), and the area of the rectangle gives you all the terms you need! In real-world applications, the concept of squaring binomials emerges during calculations in physics and engineering, particularly in determining areas or optimizing designs. For instance, when creating a rectangular garden, understanding the area formula can make a significant difference in planning and resource allocation!