Question

what is an Algebraic Identities ?
How to verify algebraic identity?
What is the difference between an algebraic expression and identities?​

Answer 1

Explanation:

An algebraic identity is an equality that holds for any values of its variables. For example, the identity ( x + y ) 2 = x 2 + 2 x y + y 2 (x+y)^2 = x^2 + 2xy + y^2 (x+y)2=x2+2xy+y2 holds for all values of x and y.

Algebraic identity (a+b)2 = a2 + 2ab + b2 is verified. The identity (a+b)2 = a2 + 2ab + b2 is verified by cutting and pasting of paper. This identity can be verified geometrically by taking other values of a and b.

In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.

Answer 2

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what is an Algebraic Identities?

Explore the world of algebraic identities by going through its various aspects and properties. Find answers to questions like what are identities, how they are formed, easy ways to remember identities, commonly used algebraic identities, and discover more interesting facts around them.

Identity means that the left-hand side of the equation is identically equal to the right-hand side, for all values of the variables.

Algebraic Identities:-

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

• How to verify algebraic identity?

• The algebraic identities are verified using the substitution method. In this method, substitute the values for the variables and perform the arithmetic operation. Another method to verify the algebraic identity is the activity method. In this method, you would need a prerequisite knowledge of Geometry and some materials are needed to prove the identity.

• What is the difference between an algebraic expression and identities?

• An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.

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