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Simplifying Algebraic Expressions: (x + 1/2)^2 + 2^5(x + 1/2) - 16
In this article, we will discuss how to simplify the algebraic expression (x + 1/2)^2 + 2^5(x + 1/2) - 16. This expression may seem complex at first, but by applying the correct order of operations and using algebraic properties, we can simplify it to a more manageable form.
Step 1: Evaluate the Exponentiation
First, let's evaluate the exponentiation 2^5. This is equal to 2 multiplied by itself 5 times, which is equal to 32.
Step 2: Expand the Square
Next, let's expand the square (x + 1/2)^2. Using the formula for the square of a binomial, we get:
(x + 1/2)^2 = x^2 + 2(x)(1/2) + (1/2)^2
= x^2 + x + 1/4
Step 3: Rewrite the Expression
Now, let's rewrite the original expression by replacing (x + 1/2)^2 with x^2 + x + 1/4 and 2^5 with 32:
x^2 + x + 1/4 + 32(x + 1/2) - 16
Step 4: Combine Like Terms
Finally, let's combine like terms:
x^2 + x + 1/4 + 32x + 16 - 16
= x^2 + 33x + 1/4
And that's the simplified form of the original expression!
