**Introduction of 9th grade algebra 1 :**

Algebra 1 is a branch of 9th grade mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, and with functions that input one vector and output another, according to certain rules. These functions are linear maps or linear transformations and are often represented by matrices. Algebra 1 is a central to modern mathematics and its applications. An elementary application of linear algebra 1 is to the solution of systems of linear equations in several unknowns. now we going to study about the 9th grade algebra.-source (wikipedia)

**Algebraic Identities**

In algebra 1 we used to study about certain algebraic equations is called algebraic identities.

An algebraic equation used to study more variables such as,

Algebraic identity for (x + a)(x + b)

By using the distributive properties of numbers,

(x + a )(x + b ) = x(x + b) + a(x + b) = x^{2} + xb + ax + ab

= x^{2} + ax + bx + ab= x^{2} + (a + b)x + ab.

Thus we get (x + a)(x + b) ≡ x2 + (a + b) x + ab

** Factorization of 9th grade algebra 1**

In algebra 1 we process of writing a polynomial as a product of two or more simpler polynomials is called factorization..

** Factorize x ^{2} – 2xy – x + 2y.**

** Solution:**

The terms of the expression do not have a common factor. However, we observe that the terms can be grouped as follows:

x2 – 2xy – x + 2y = (x2 – 2xy) – (x – 2y)

= x(x – 2y) + (–1) (x – 2y)

=(x – 2y) [x + (–1)] = (x – 2y) (x – 1).

In Algebra 1 we add two polynomials by adding the coefficients of the like powers are called Addition of Polymomials.

** Example of 9th grade algebra 1:**

Find the sum of 2x^{4} – 3x^{2} + 5x + 3 and 4x + 6x^{3} – 6x^{2} – 1.

** Solution:**

Using associative and distributive properties of real numbers, we obtain

(2x^{4} – 3x^{2} + 5x + 3) + (6x^{3} – 6x2 + 4x – 1) = 2x^{4} + 6x^{3} – 3x^{2} – 6x^{2} + 5x + 4x + 3 – 1

= 2x^{4} + 6x^{3} – (3+6)x^{2} + (5+4)x + 2

= 2x^{4} + 6x^{3} – 9x^{2} + 9x + 2.

The following scheme is helpful in adding two polynomials

2x^{4} + 0x^{3} – 3x^{2} + 5x + 3

0x^{4} + 6x^{3} – 6x^{2} + 4x – 1

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** 2x ^{4} + 6x^{3}– 9x^{2} + 9x + 2**