%5E2-expand.jpeg "(2x+4)^2 Expand")
Expanding (2x + 4)^2
Expanding a squared binomial like (2x + 4)^2 involves multiplying the binomial by itself. Here's how to do it:
Understanding the Concept
- Binomial: A polynomial with two terms, like (2x + 4).
- Squared: Means multiplying the binomial by itself.
Expanding using FOIL
The FOIL method helps us systematically multiply each term of the first binomial by each term of the second binomial:
- First: 2x * 2x = 4x²
- Outer: 2x * 4 = 8x
- Inner: 4 * 2x = 8x
- Last: 4 * 4 = 16
Combining the terms:
4x² + 8x + 8x + 16
Simplifying the expression:
4x² + 16x + 16
Alternative Method: Using the Square of a Sum Formula
We can also use the algebraic formula:
(a + b)² = a² + 2ab + b²
In our case, a = 2x and b = 4:
(2x + 4)² = (2x)² + 2(2x)(4) + 4²
Expanding the terms:
4x² + 16x + 16
Conclusion
Both methods lead to the same expanded form: 4x² + 16x + 16. Understanding these methods allows you to expand any squared binomial efficiently.