%5E2%2B(x%2B3)%5E2-5(x%2B7)(x-7).jpeg "(2x-1)^2+(x+3)^2-5(x+7)(x-7)")
Simplifying the Expression: (2x-1)^2 + (x+3)^2 - 5(x+7)(x-7)
This article will guide you through the process of simplifying the given algebraic expression: (2x-1)^2 + (x+3)^2 - 5(x+7)(x-7).
Expanding the Squares
First, we need to expand the squares using the formula (a+b)^2 = a^2 + 2ab + b^2:
- (2x-1)^2 = (2x)^2 + 2(2x)(-1) + (-1)^2 = 4x^2 - 4x + 1
- (x+3)^2 = x^2 + 2(x)(3) + 3^2 = x^2 + 6x + 9
Expanding the Product
Next, we expand the product using the difference of squares formula (a+b)(a-b) = a^2 - b^2:
- 5(x+7)(x-7) = 5(x^2 - 7^2) = 5(x^2 - 49)
Combining the Terms
Now, we can substitute the expanded terms back into the original expression and combine like terms:
(2x-1)^2 + (x+3)^2 - 5(x+7)(x-7) = (4x^2 - 4x + 1) + (x^2 + 6x + 9) - 5(x^2 - 49)
= 4x^2 - 4x + 1 + x^2 + 6x + 9 - 5x^2 + 245
= (4x^2 + x^2 - 5x^2) + (-4x + 6x) + (1 + 9 + 245)
= 2x + 255
Final Result
Therefore, the simplified form of the expression (2x-1)^2 + (x+3)^2 - 5(x+7)(x-7) is 2x + 255.