(y%2B8)%2B(y-8)(y%2B1).jpeg "(y+1)(y+8)+(y-8)(y+1)")
Simplifying the Expression (y+1)(y+8)+(y-8)(y+1)
This article will guide you through the steps of simplifying the expression (y+1)(y+8)+(y-8)(y+1).
Step 1: Expand the Products
We begin by expanding each of the products using the FOIL method (First, Outer, Inner, Last):
- (y+1)(y+8) = y² + 8y + y + 8 = y² + 9y + 8
- (y-8)(y+1) = y² + y - 8y - 8 = y² - 7y - 8
Step 2: Combine Like Terms
Now we have: y² + 9y + 8 + y² - 7y - 8
Combining the like terms:
- y² + y² = 2y²
- 9y - 7y = 2y
- 8 - 8 = 0
Step 3: The Simplified Expression
Putting it all together, the simplified expression is:
(y+1)(y+8)+(y-8)(y+1) = 2y² + 2y
Conclusion
By expanding the products and combining like terms, we have successfully simplified the expression (y+1)(y+8)+(y-8)(y+1) to 2y² + 2y. This process demonstrates how algebraic manipulation can lead to a more concise and manageable form of an expression.