What is factoring the difference of two squares?
Mason Cooper
Published Apr 22, 2026
What is factoring the difference of two squares?
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
What is difference of two squares in maths?
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. One thing to note about this theorem is that it does not apply to the SUM of squares.
What is the example of difference of two squares?
Solution.
| 1. Common Factor | 2(a + b) | 2a + 2b |
| 2. Quadratic Trinomial | (x + 2)(x + 3) | x2 + 5x + 6 |
| 3. Perfect Square Trinomial | (x − 5)2 | x2 − 10x + 25 |
| 4. The Difference of Two Squares | (x + 5)(x − 5) | x2 − 25 |
Which of the following 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.
Why is it called difference of two squares?
where one perfect square is subtracted from another, is called a difference of two squares. It arises when (a − b) and (a + b) are multiplied together. This is one example of what is called a special product.
Why is it called the difference of two squares?
How was the factor of the difference of two squares and the product and the sum of two terms related?
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.
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.
How do you factor the sum and difference of two squares?
If two terms in a binomial are perfect squares separated by subtraction, then you can factor them. To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared terms, then the sum and the difference of the two square roots factor the binomial.
How do you factor polynomial using difference of squares?
To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared terms, then the sum and the difference of the two square roots factor the binomial. For example: Example 1: Find the square roots of the two terms that are perfect squares. Write the factorization as the sum and difference of the square roots.
What is the formula for the sum of two squares?
In number theory, the sum of two squares theorem says when an integer n > 1 can be written as a sum of two squares, that is, when n = a2 + b2 for some integers a, b.
What is the formula of the difference of two squares?
The difference of squares method is an easy way to factor a polynomial that involves the subtraction of two perfect squares . Using the formula a 2 − b 2 = ( a − b ) ( a + b ) {\\displaystyle a^{2}-b^{2}=(a-b)(a+b)} , you simply need to find the square root of each perfect square in the polynomial, and substitute those values into the formula .
