The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots.

Which numbers can be written as the difference of two squares?

Since a – b = 1, b = a-1, so b = frac{p+1}{2} – 1 = frac{p-1}{2}. Thus, any odd prime can be written as the difference of two squares. Any square number n can also be written as the difference of two squares, by taking a = sqrt{n} and b = 0.

What is the result when you square a binomial?

The square of a binomial is the sum of: the square of the first terms, twice the product of the two terms, and the square of the last term. I know this sounds confusing, so take a look.. If you can remember this formula, it you will be able to evaluate polynomial squares without having to use the FOIL method.

Which binomial is a difference of two squares?

When we have a binomial (a mathematical expression with two terms) that is the difference of two squared terms, we can factor the binomial as the product of a difference and sum. This is called the difference of squares formula and is written as a2 – b2 = (a – b)(a + b).

How will you factor sum and difference of two cubes?

The sum or difference of two cubes can be factored into a product of a binomial times a trinomial. That is, x3+y3=(x+y)(x2−xy+y2) and x3−y3=(x−y)(x2+xy+y2) .

How do you write something as a difference?

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value. The product of this sum is the difference between the two numbers.

Can 4 be written as the difference of two squares?

Integers that are multiples of 4 can also be expressed as the difference of two squares. The two integers in these expressions differ by 2.

What is the form of difference of squares identity?

Identity. The difference of two squares identity is ( a + b ) ( a − b ) = a 2 − b 2 (a+b)(a-b)=a^2-b^2 (a+b)(a−b)=a2−b2.

When an expression is a difference of two squares What are its factors?

To factor a difference of two squares, you simply take the expressions that are squared (in the example the expressions 3 x 3x 3x and 4) and put both of them (in the given order) into the terms in both factors of the given binomial.

What is the sum and difference of two terms?

It is stated as: The product of the binomial sum and difference is equal to the square of the first term minus the square of the second term. Worked-out examples on the product of sum and difference of two binomials: 1.

When we multiply the sum and difference of the same two terms we note that the product is called?

The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared. Thus, this resulting binomial is called a difference of squares.

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