Math Problem Statement

factorise 4x au carre - 5

Solution

To factorize the quadratic expression 4x254x^2 - 5, we recognize that it fits the form of a difference of squares:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

Here:

  • a2=4x2a^2 = 4x^2, so a=2xa = 2x
  • b2=5b^2 = 5, so b=5b = \sqrt{5}

Using the difference of squares formula, we factor it as:

4x25=(2x5)(2x+5)4x^2 - 5 = (2x - \sqrt{5})(2x + \sqrt{5})

This is the factorized form.

Would you like more details on the difference of squares or any other part of the solution?

Related Questions:

  1. How can you identify a difference of squares in a quadratic expression?
  2. What if the expression was 4x2+54x^2 + 5? How would that be factorized?
  3. What is the importance of recognizing patterns in factoring polynomials?
  4. How do you apply factoring techniques to solve quadratic equations?
  5. Can you explain the general steps for factoring trinomials?

Tip: Always look for common factors before applying other factoring methods like difference of squares or trinomials.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Difference of Squares

Formulas

a^2 - b^2 = (a - b)(a + b)

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 9-11