Question

What are algebraic identities?

Answer 1

Determining the algebraic identities.

An algebraic identity consists of algebraic operations and is equality, which is true for all values of the variables in the equality.

These also are employed in polynomial factorization, in the calculation of algebraic expressions, etc

Some Algebraic identities:

$$\begin{gathered} {(a+b)}^2=a^2+2ab+b^2 \\ {(a-b)}^2=a^2-2ab+b^2 \\ {a}^2–b^2=(a+b)(a–b) \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ (x+a)(x–b)=x^2+(a–b)x–ab \\ (x–a)(x+b)=x^2+(b–a)x–ab \\ (x–a)(x–b)=x^2–(a+b)x+ab \\ {(a+b)}^3=a^3+b^3+3ab(a+b) \\ {(a–b)}^3=a^3–b^3–3ab(a–b) \end{gathered}$$