%5E2.jpeg "(2x^2-5)^2")
Expanding (2x^2 - 5)^2
The expression (2x^2 - 5)^2 represents the square of a binomial. To expand it, we can utilize the following algebraic identity:
** (a - b)^2 = a^2 - 2ab + b^2**
Step 1: Identify a and b
In our case, a = 2x^2 and b = 5.
Step 2: Apply the formula
Substituting the values of a and b into the identity, we get:
(2x^2 - 5)^2 = (2x^2)^2 - 2(2x^2)(5) + (5)^2
Step 3: Simplify
Expanding and simplifying the expression:
(2x^2 - 5)^2 = 4x^4 - 20x^2 + 25
Therefore, the expanded form of (2x^2 - 5)^2 is 4x^4 - 20x^2 + 25.
Note: This expression is a polynomial of degree 4, as the highest power of x is 4. It is a quadratic in x^2, meaning it can be expressed in the form ax^4 + bx^2 + c.