It is read as the \$a\$ plus \$b\$ times \$a\$ minus \$b\$ is equal to the \$a\$ squared minus \$b\$ squared.

You are watching: (a-b)(a+b)

Introduction

Let the 2 literals \$a\$ and \$b\$ be two variables.

The addition of them kind a binomial \$a+b\$.The individually of them kind another binomial \$a-b\$.

The two binomials space sum and difference basis binomials. The authorized of these 2 binomials in multiplication is a special case in mathematics. Hence, the product of castle is generally dubbed as the distinct product the binomials or the special binomial product in algebra.

\$(a+b) imes (a-b)\$

The product that the binomials \$a+b\$ and also \$a-b\$ is just written in the following kind in mathematics.

\$implies\$ \$(a+b)(a-b)\$

The unique product the the binomials \$a+b\$ and \$a-b\$ is equal to the distinction of squares the the terms \$a\$ and \$b\$.

\$,,, herefore,,,,,,\$ \$(a+b)(a-b)\$ \$,=,\$ \$a^2-b^2\$

The mathematics equation expresses that the product the sum and difference communication binomials, which contain the exact same terms is same to the distinction of them.

It is supplied as a formula in mathematics. Hence, it is dubbed an algebraic identity.

Usage

It is largely used together a formula to leveling an expression when the expression satisfies the adhering to conditions.

The two binomials must be created by the 2 variables.The 2 variables should be associated with opposite indications in the binomials.Verification

Let’s examine this math equation by acquisition some worths for verification. Take \$a = 7\$ and \$b = 3\$, and find the values of both sides of the equation.

\$(1). ,,,\$ \$(a+b)(a-b)\$ \$,=,\$ \$(7+3)(7-3)\$ \$,=,\$ \$10 imes 4\$ \$,=,\$ \$40\$

\$(2). ,,,\$ \$a^2-b^2\$ \$,=,\$ \$(7)^2-(3)^2\$ \$,=,\$ \$49-9\$ \$,=,\$ \$40\$

\$,,, herefore ,,,,,,\$ \$(7+3)(7-3)\$ \$,=,\$ \$(7)^2-(3)^2\$ \$,=,\$ \$40\$

Therefore, we can use this mathematical equation together an algebraic identification in mathematics.

Example

Simplify \$(3p+4q)(3p-4q)\$

Let us inspect the given expression to know whether we deserve to use \$a\$ add to \$b\$ time \$a\$ minus \$b\$ formula or not.

\$3p\$ and also \$4q\$ space the terms in both binomials in the multiplication.The terms \$3p\$ and also \$4q\$ are connected by the opposite indicators plus and minus in the determinants of the multiplication.

The two conditions of \$(a+b)(a-b)\$ formula space satisfied. So, we have the right to use the formula because that simplifying given algebraic expression.

Take \$a = 3p\$ and also \$b = 4q\$ and substitute them in the \$a+b\$ times \$a-b\$ formula.

\$(a+b)(a-b) ,=, a^2-b^2\$

\$implies\$ \$(3p+4q)(3p-4q)\$ \$,=,\$ \$(3p)^2-(4q)^2\$

\$,,, herefore,,,,,,\$ \$(3p+4q)(3p-4q)\$ \$,=,\$ \$9p^2-16q^2\$

Thus, we use the \$(a+b)(a-b)\$ unique binomial product dominion in mathematics.

Proofs

There room two possible ways to have the \$a\$ to add \$b\$ time \$a\$ minus \$b\$ formula in mathematics.

Algebraic method

Learn just how to prove the \$a\$ plus \$b\$ time \$a\$ minus \$b\$ algebraic identification by the multiplication that algebraic expressions.

See more: Watch The Walking Dead Season 1 Episode 6 Full Episode Free Online

Geometric method

Learn how to prove the \$a\$ to add \$b\$ time \$a\$ minus \$b\$ algebraic law geometrically indigenous the areas of geometric shapes.