Difference Of Squares Formula

Difference of Squares Formula

The Difference Of Squares Formula is demonstrated by A2- B2 = (A + B) (A – B). The study, manipulation, and analysis of a wide variety of mathematical symbols are the focus of the mathematical field of Algebra. It is the study of unknowable amounts, which are frequently represented by variables in Mathematics. Algebra contains a variety of formulas and identities for the purpose of examining situations involving variables. Additionally, it has several sub-branches, such as Commutative Algebra, Advanced Algebra, and Linear Algebra. Equations with algebraic identities have the same value on the left and right sides of the equation, respectively. Contrary to algebraic expressions, algebraic identities satisfy the values of all the variables. The difference of squares occupies a prominent position in Algebra despite the fact that there are many other algebraic identities.

A quadratic equation is a unique equation that typically takes the form ax2 + bx + c = 0, with x being an unknown, a being a non-zero number, and b and c being any two numbers. This equation’s graph is always a parabola, which may or may not cross the x-axis. It looks somewhat like a soup bowl and can be either right-side up or upside down. A quadratic equation can be factored by dividing it into smaller units (called factors) that can then be multiplied together to create the original quadratic equation. When a number or integer (not a fraction) is multiplied by itself, a square is produced. The difference (or change) of two algebraic variables’ squares is what the formula’s name suggests. For instance, a and b are two variables. Then, a2 – b2 would be the difference between their squares. 

Formula to Calculate the Difference of Squares

The expression a2 – b2 is equal to the product of the sum and difference of the variables for any two algebraic variables, a and b, according to the difference of squares formula. This identity is frequently employed to make complex algebraic expressions simpler. The various applications of this identity include algebraic factorisation, the quadratic sieve, and integer factorisation. 

What Is the Difference of Squares Formula?

Mathematicians typically use the algebraic identity of the difference of squares as a formula in two situations. By computing the product of the sum and difference of the two quantities, it is used to determine the difference of squares of two quantities. It can also be used to factorise the squared differences of two quantities in order to simplify expressions and solve equations. If for example, a quadratic equation can be factored into two binomials. One of which is a sum of the square roots and the other is a difference of the square roots, according to the difference of two Squares theorem, if it can be written as a difference between two squares. Any expression can be solved using this method as long as there is a difference between the squares.

Solved Examples Using Difference of Squares Formula

It is necessary for students to practice examples specific to the Difference Of Squares Formula. Practising questions related to the Difference Of Squares Formula will assist students to prepare well for the Mathematics examination. The Extramarks learning portal has NCERT solutions that can be used to solve questions in a proper manner.