2.jpeg "(y+8)2")
Expanding (y + 8)²
The expression (y + 8)² represents the square of the binomial (y + 8). To expand this expression, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial by each term in the second binomial.
- First: y * y = y²
- Outer: y * 8 = 8y
- Inner: 8 * y = 8y
- Last: 8 * 8 = 64
Now, we combine like terms: y² + 8y + 8y + 64 = y² + 16y + 64
Using the Square of a Binomial Pattern
The square of a binomial pattern states: (a + b)² = a² + 2ab + b²
In our case, a = y and b = 8. Substituting these values into the pattern:
y² + 2(y)(8) + 8² = y² + 16y + 64
Conclusion
Both methods lead to the same expanded form of (y + 8)²: y² + 16y + 64. The choice of method depends on personal preference. However, understanding both methods will help you expand similar expressions efficiently.