%5E2.jpeg "(y-7)^2")
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.