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No. If the two numbers are consecutive then the difference of their squares need not be factorisable.

For example, 4^3 - 3^3 = 16 - 9 = 7, which is a prime.

If the smaller number is a then this simply requires that 2a+1 is a prime.

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Q: Does the difference of two squares number always factorable?
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How do you find the number of solutions in a quadratic equation?

Factoring by the AC method, difference of squares, perfect square trinomial. If not factorable by those ways, you can use the quadratic formula. You can also find zeros by synthetic division. If there are not any real solutions, then the solutions are said to be complex, they do not cross the x axis.


What is the difference between an equilateral triangle and an equilateral square?

The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.


What is different about a perfect square and a difference of two squares?

"Perfect square" means that you square a whole number. Sometimes simply called "square" or "square number". "Difference of two squares" is the result of subtracting one such square from another. In most cases, the difference will not itself be a square.


The difference of two even number is always an even number?

Yes, the difference between two even numbers is always an even number.


Is the difference of a rational number and an irrational number always ratioal?

No, it is always irrational.

Related questions

How do you find the number of solutions in a quadratic equation?

Factoring by the AC method, difference of squares, perfect square trinomial. If not factorable by those ways, you can use the quadratic formula. You can also find zeros by synthetic division. If there are not any real solutions, then the solutions are said to be complex, they do not cross the x axis.


What numbers always have an even number of factors?

All positive integers which are not perfect squares.


What number is equal to one-third of the difference between the squares of ten and eight?

one third of the difference between ten and a number


What is the difference between an equilateral triangle and an equilateral square?

The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.The difference is in the number of sides. A triange has 3 sides, a square has 4 sides.By the way, all squares are equilateral by definition.


Can you express every odd prime number as the difference of two squares?

Every odd number greater than one is the difference of two squares. This includes all the odd prime numbers. To find the two numbers whose difference of squares equals a particular odd number, divide the odd number by 2. The two numbers are the integers immediately below and above that dividend. For example, 17 is the difference of two squares. Divide 17 by 2 and get 8.5. The two numbers are 8 and 9. 92 - 82 = 81 - 64 = 17.


What is different about a perfect square and a difference of two squares?

"Perfect square" means that you square a whole number. Sometimes simply called "square" or "square number". "Difference of two squares" is the result of subtracting one such square from another. In most cases, the difference will not itself be a square.


The difference of two even number is always an even number?

Yes, the difference between two even numbers is always an even number.


Can you express the prime number 23 as a difference of two squares?

Yes. 23 = 122 - 112


Is the difference of a rational number and an irrational number always ratioal?

No, it is always irrational.


Is 18 a factor of 7?

No. 7 is a prime number divisible by 1 and itself, so, not really factorable.


Is the difference of 2 whole numbers always a whole number?

Yes, the difference of two whole numbers is always a whole number.


If you square two consecutive whole numbers and substract from the larger Is it possible that the difference is an even number?

No. The difference between the squares of two successive integers is always an odd number, the sum of your two original numbers eg 42 - 32 = 16 - 9 = 7 = 4 + 3. Another example 472 - 462 = 2209 - 2116 = 93 = 47 + 46. The proof is straightforward, based on the squares of n and n - 1...