-squared.jpeg "(x+7) Squared")
Understanding (x + 7)²
In mathematics, squaring a binomial like (x + 7) involves multiplying it by itself. This can be done using the FOIL method or by applying the square of a binomial formula. Let's explore both approaches:
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. It's a mnemonic device to help remember the steps of multiplying two binomials:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 7 = 7x
- Inner: Multiply the inner terms of the binomials: 7 * x = 7x
- Last: Multiply the last terms of each binomial: 7 * 7 = 49
Now, combine the results: x² + 7x + 7x + 49. Finally, simplify by combining like terms: x² + 14x + 49
Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)² = a² + 2ab + b²
Applying this to (x + 7)², we have:
- a = x
- b = 7
Therefore, (x + 7)² = x² + 2(x)(7) + 7²
Simplifying this gives us: x² + 14x + 49
Conclusion
Both methods lead to the same result: (x + 7)² = x² + 14x + 49. This expansion is important for simplifying expressions, solving equations, and understanding the behavior of quadratic functions.