How to Identify and Factor Perfect Square Trinomials - GED Math

Identifying Perfect Square Trinomials

• 💡 To determine if an expression like 36x^2 + 120x + 100 is a perfect square trinomial, take the square root of the leading coefficient (36, which is 6) and the constant term (100, which is 10).
• 🎯 Multiply these two results (6 * 10 = 60) and then double the product (60 * 2 = 120).
• ✅ If this doubled product matches the middle coefficient (120x), then the expression is a perfect square trinomial.

Factoring Perfect Square Trinomials

• 🔑 The formula for a perfect square trinomial is a^2 + 2ab + b^2 = (a + b)^2.
• 🧠 In the example 36x^2 + 120x + 100, a^2 is 36x^2 (so a = 6x) and b^2 is 100 (so b = 10).
• 🚀 Therefore, the factored form is (6x + 10)^2.

Simplifying Factored Expressions

• 🧩 When factoring (6x + 10)^2, a Greatest Common Factor (GCF) of 2 can be taken from each binomial: 2(3x + 5).
• 📈 Since the expression is squared, this becomes [2(3x + 5)]^2, which simplifies to 2^2 * (3x + 5)^2, or 4(3x + 5)^2.
• 🎯 The final factored form, considering the GCF, is 4(3x + 5)^2.