Solving Quadratic Equations by Taking Square Roots – Practice Problems

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We will learn on how to factor the difference of two squares. Like 4x² – 25 = 0, for example. When factoring such a difference of two squares, we end up always getting the product of the sum and the difference of the same two terms.
For instance, with 4x² – 25 = 0, we end up taking the square roots of 4x² and 25 to get 2x and 5, respectively. Then 2x and 5 are the terms which appear in our product. In other words, the factorization of 4x² – 25 = 0 is (2x + 5)(2x – 5) = 0, or (2x – 5)(2x + 5) = 0, as the commutative property of real numbers states that order of factors in multiplication or addition does not matter. To know more about this method for factoring the difference of two squares, you can watch this video.

This method for factoring the difference of two squares can be represented in algebraic expressions as follows:

Product of Sum and Difference of Two Squares: (a + b)( a – b) = a² – b²

Factors of Difference of Two Squares: a² – b² = (a + b)(a – b)

where a and b are any real numbers.

Solve quadratic equations in one variable.


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Exercises in this Practice Problem
Explain how to factor quadratic equations which are a difference of two squares.
Factor the quadratic equation.
Find the errors in Rap-Punzel's calculations.
Identify which factorizations of the equations are correct.
Explain any differences between $16x^4 -81=0$ and $ax^2 +bx +c=0$.
Determine the factored equation.