Question

Write all and identity related to Algebra .​

Answer 1

Answer:

Algebraic identities are algebraic equations that are true for all the variables present in them. These identities contain constants and variables on both sides of the equation. When we factorize a polynomial, we often use these algebraic identities. A polynomial function is an algebraic expression that contains more than one term. Examples of polynomials include binomials and trinomials.

Step-by-step explanation:

Square of a Binomial

(a \pm b) ^ 2 = a ^ 2 \pm 2 \cdot a \cdot b + b ^2

The above algebraic identity is also known as a quadratic identity because after expansion and setting the equation equal to zero, we get a quadratic formula. The sign with 2ab will depend upon the addition and subtraction sign between a and b.

Using the above algebraic identity, we will solve some examples. You will see that any value of the variable satisfied both sides of the equation.

Example 1

(x + 3) ^ 2

Use the algebraic identity (a \pm b) ^ 2 = a ^ 2 \pm 2 \cdot a \cdot b + b ^2 to open up the parentheses of this question.

= x ^ 2 + 2 \cdot x \cdot 3 + 3 ^ 2

Since, there is a positive sign between x and 3, so we will use a positive sign with 2(x)(3).

= x ^ 2 + 6 x + 9

The answer x ^ 2 + 6 x + 9 is also a quadratic equation since the standard form of a quadratic equation is a x ^2 + bx + c. In this answer, the leading coefficient a = 1 , the middle coefficient b = 6 and the last constant term c = 9. The last term of the quadratics is a constant term in which no variable is involved.

Hence, (x + 3) ^ 2 = x ^ 2 + 6 x + 9. It means that all the variables hold true for both sides of this algebraic equation.

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Answer 2

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