(a-1/2a)2 Is Equal To

2 min read Jun 16, 2024
(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.

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