Which polynomial is a difference of two squares?

Which polynomial is a difference of two squares?

x2 – 25
Answer: The polynomial that is the difference of two squares is x2 – 25. Let us see how we will use the concept of factoring polynomials that are used to express the differences between two perfect squares.

What are the conditions for the difference of two squares?

Whenever you have a binomial with each term being squared (having an exponent of 2), and they have subtraction as the middle sign, you are guaranteed to have the case of difference of two squares.

How do you tell if a binomial is a difference of two squares?

A binomial is a Difference of Squares if both terms are perfect squares. Recall we may have to factor out a common factor first. If we determine that a binomial is a difference of squares, we factor it into two binomials. The first being the square root of the first term minus the square root of the second term.

Is the sum and difference of two polynomials always a polynomial?

Explanation: If you add, subtract or multiply any two polynomials then the result will be a polynomial. When adding or subtracting two polynomials you typically group together similar terms and add or subtract their coefficients. For any polynomial P : P+0=0+P=P.

Is a polynomial times a polynomial always a polynomial?

When two polynomials are multiplied, each term of the first polynomial is multiplied by each term of the second polynomial. The result is always a polynomial, regardless what the coefficients might be of any of the terms, including the leading coefficients.

How can you tell if a polynomial is a perfect square?

When a polynomial is multiplied by itself, then it is a perfect square. Example – this polynomial ax2 + bx + c; if b2 = 4ac is a perfect square.

What is the formula for factoring the difference of squares?

Check if the terms have the greatest common factor (GCF) and factor it out. Remember to include the GCF in your final answer

  • Determine the numbers that will produce the same results and apply the formula: a 2 – b 2 = (a+b) (a – b) or (a – b) (a
  • Check whether the remaining terms can be factored any further.
  • Which expressions are differences of squares?

    A difference of squares is an expression like the following: A^2 – B^2. The following polynomials are differences of squares: b^2 – 49, 4t^2 – 9, c^2 – 25d^2. For an expression to be written as a difference of squares, it must be of the form: A^2 – B^2 = (A + B)(A – B)

    How to find the difference of squares?

    The procedure to use the difference of squares calculator is as follows: Enter the “a” and “b” value in the input field Now click the button “Calculate Difference of Squares” to get the result Finally, the difference between the two squared numbers will be displayed in the output field

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