$a^2-b^2$ $\,=\,$ $(a+b)(a-b)$
$(a+b)(a-b)$ is an algebraic identity and represents the product of two binomials, formed by the summation and subtraction of the literals $a$ and $b$. In mathematics, it is used to write the product of the binomial factors as subtraction of the squares of the literals and vice-versa.
The $a$ squared minus $b$ squared algebraic identity can be derived in two distinct methods.
Learn how to prove the $a$ square minus $b$ square rule mathematically in algebraic approach.
Learn how to derive the $a$ squared minus $b$ squared law mathematically in geometric method.
Take $a \,=\, 6$ and $b \,=\, 4$. Now, let’s verify the $a$ square minus $b$ square algebraic identity by substituting the values in both side expressions.
$(1).\,\,$ $a^2-b^2$ $\,=\,$ $6^2-4^2$ $\,=\,$ $36-16$ $\,=\,$ $20$
$(2).\,\,$ $(a+b)(a-b)$ $\,=\,$ $(6+4)(6-4)$ $\,=\,$ $10 \times 2$ $\,=\,$ $20$
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