## Understanding (y-7)^2

(y-7)^2 is a mathematical expression that represents the **square of the binomial (y-7)**. In other words, it means multiplying the binomial by itself:

**(y-7)^2 = (y-7) * (y-7)**

To simplify this expression, we can use the **FOIL method** (First, Outer, Inner, Last):

**First:**y * y = y^2**Outer:**y * -7 = -7y**Inner:**-7 * y = -7y**Last:**-7 * -7 = 49

Adding all these terms together, we get:

**(y-7)^2 = y^2 - 7y - 7y + 49**

Finally, combining like terms, we get the simplified expression:

**(y-7)^2 = y^2 - 14y + 49**

### Key Points:

**Squaring a binomial**means multiplying it by itself.**FOIL method**is a helpful tool for multiplying binomials.**Simplifying the expression**involves combining like terms.

### Applications:

Understanding how to expand and simplify expressions like (y-7)^2 is crucial in various areas of mathematics, including:

**Algebra:**Solving equations and inequalities.**Calculus:**Finding derivatives and integrals.**Geometry:**Calculating areas and volumes.

By mastering the concept of squaring binomials, you'll be able to tackle more complex mathematical problems and gain a deeper understanding of mathematical concepts.