Math Problem Statement

X^2+4x+4

Solution

The expression x2+4x+4x^2 + 4x + 4 is a quadratic expression. Let's solve it by factoring.

The expression can be rewritten as:

x2+4x+4=(x+2)(x+2)=(x+2)2x^2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)^2

Thus, the factored form is (x+2)2(x + 2)^2.

If you were solving x2+4x+4=0x^2 + 4x + 4 = 0, the solution would be:

(x+2)2=0    x=2(x + 2)^2 = 0 \implies x = -2

Let me know if you would like any further explanation!

Related questions:

  1. How do you solve a quadratic equation by completing the square?
  2. What is the quadratic formula and when should it be used?
  3. How do you find the vertex of a quadratic function?
  4. What is the significance of the discriminant in a quadratic equation?
  5. How does factoring relate to finding the roots of a quadratic equation?

Tip: Always check if a quadratic expression can be factored before using the quadratic formula. This can save time!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Expressions
Factoring

Formulas

Factoring quadratic expressions
Quadratic equation formula

Theorems

Zero Product Property

Suitable Grade Level

Grades 8-10