(x%2B10).jpeg "(x+10)(x+10)")
Expanding (x + 10)(x + 10)
The expression (x + 10)(x + 10) is a product of two identical binomials. This type of expression is called a perfect square trinomial. To expand it, we can use the FOIL method or the distributive property.
Using FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial with each term in the second binomial:
- First: x * x = x²
- Outer: x * 10 = 10x
- Inner: 10 * x = 10x
- Last: 10 * 10 = 100
Combining the terms, we get: x² + 10x + 10x + 100
Finally, we simplify the expression by combining the like terms: x² + 20x + 100
Using the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend in the sum by that number and then adding the products.
We can apply this property to our expression:
(x + 10)(x + 10) = (x + 10) * x + (x + 10) * 10
Then, we distribute again:
x * x + 10 * x + x * 10 + 10 * 10
This gives us the same result as before: x² + 10x + 10x + 100
Finally, we simplify: x² + 20x + 100
Conclusion
Both methods lead to the same expanded form of (x + 10)(x + 10), which is x² + 20x + 100. This is a perfect square trinomial because it represents the square of the binomial (x + 10).