Math Problem Statement

(a-1/2)^2 factoring answer

Solution

To factor the expression (a12)2(a - \frac{1}{2})^2, notice that it is already written in the form of a perfect square trinomial.

However, if you need to expand it, you would apply the formula for a binomial square:

(a12)2=a22a12+(12)2(a - \frac{1}{2})^2 = a^2 - 2 \cdot a \cdot \frac{1}{2} + \left(\frac{1}{2}\right)^2

Simplifying this gives:

(a12)2=a2a+14(a - \frac{1}{2})^2 = a^2 - a + \frac{1}{4}

So, the factored form of a2a+14a^2 - a + \frac{1}{4} is (a12)2(a - \frac{1}{2})^2.

Questions:

  1. How would you factor (a+13)2(a + \frac{1}{3})^2?
  2. Can you factor (a3)2(a - 3)^2?
  3. What is the expanded form of (x23)2(x - \frac{2}{3})^2?
  4. How would you factor b22b+1b^2 - 2b + 1?
  5. What is the factored form of 4a24a+14a^2 - 4a + 1?

Tip: When factoring perfect square trinomials, always check if the middle term is twice the product of the square roots of the first and last terms.

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Math Problem Analysis

Mathematical Concepts

Algebra
Perfect Square Trinomials
Binomial Squares

Formulas

Binomial square formula

Theorems

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Suitable Grade Level

Grades 7-9