%5E2%2B(x%2B5)%5E2-(2x%2B10)(x-5).jpeg "(5-x)^2+(x+5)^2-(2x+10)(x-5)")
Simplifying the Expression: (5-x)^2 + (x+5)^2 - (2x+10)(x-5)
This article will guide you through the process of simplifying the given algebraic expression: (5-x)^2 + (x+5)^2 - (2x+10)(x-5)
Step 1: Expanding the Squares
We start by expanding the squared terms using the formula (a-b)^2 = a^2 - 2ab + b^2.
- (5-x)^2 = 5^2 - 2(5)(x) + x^2 = 25 - 10x + x^2
- (x+5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25
Our expression now becomes: (25 - 10x + x^2) + (x^2 + 10x + 25) - (2x+10)(x-5)
Step 2: Expanding the Product
Next, we expand the product using the distributive property (also known as FOIL): (a+b)(c+d) = ac + ad + bc + bd
- (2x+10)(x-5) = 2x(x) + 2x(-5) + 10(x) + 10(-5) = 2x^2 - 10x + 10x - 50
Substituting this back into our expression, we get: (25 - 10x + x^2) + (x^2 + 10x + 25) - (2x^2 - 10x + 10x - 50)
Step 3: Combining Like Terms
Now we combine the terms with the same powers of x:
- x^2 + x^2 - 2x^2 = 0
- -10x + 10x + 10x = 10x
- 25 + 25 + 50 = 100
Our simplified expression is: 0 + 10x + 100
Final Result
Therefore, the simplified form of the expression (5-x)^2 + (x+5)^2 - (2x+10)(x-5) is 10x + 100.