2-is-equal-to.jpeg "(a-1/2a)2 Is Equal To")
Simplifying (a - 1/2a)^2
This article will guide you through the steps of simplifying the expression (a - 1/2a)^2.
Understanding the Expression
The expression (a - 1/2a)^2 represents squaring the entire binomial (a - 1/2a). In simpler terms, it means multiplying the binomial by itself:
(a - 1/2a)^2 = (a - 1/2a) * (a - 1/2a)
Expanding the Expression
To simplify, we need to expand the expression using the FOIL method:
- First: Multiply the first terms of each binomial: a * a = a^2
- Outer: Multiply the outer terms of the binomials: a * -1/2a = -1/2a^2
- Inner: Multiply the inner terms of the binomials: -1/2a * a = -1/2a^2
- Last: Multiply the last terms of each binomial: -1/2a * -1/2a = 1/4a^2
Combining Like Terms
Now we have the expanded expression: a^2 - 1/2a^2 - 1/2a^2 + 1/4a^2
Combining like terms:
- a^2 - 1/2a^2 - 1/2a^2 + 1/4a^2 = (1 - 1/2 - 1/2 + 1/4)a^2
Simplifying the coefficients:
- (1 - 1/2 - 1/2 + 1/4)a^2 = (1/4)a^2
Final Result
Therefore, the simplified form of (a - 1/2a)^2 is (1/4)a^2.