#
__Linear Equation__

Algebraic equations are connected in a real life situations such as samgot x articles for 3 dollars and y articles for 7 dollars. Now we can connect the above in the form of equation as x+y= 3+7 so this equation becomes x+y= 10.

##
Definition of Linear Equation

An equation in which the degree of the variable is 1 is called a linear equation.

Example of a linear equation : 3x+ 5=6 ,Here the degree of the variable is 1

##
Solving Linear Equations

1.Solve for X

Find the value of x in the equation 4x+6=10

Answer : 4x=10-6

4x=4

X=

$\frac{4}{4}$
X=1

2. Solve 5x-5=5

5x=10

X=

$\frac{10}{5}$
X=2

3. solve 6x+8=-4

6x=-4-8

6x=-12

X=

$\frac{-12}{6}$
##
Linear Polynomials

A rational function is called a polynomial.

**Monomial: **A polynomial containing one term is called a monomial.

Example: 3x, 3y

^{2}, 9xyz

**Binomial:** A polynomial with two terms is called a Binomial.

Example : 5x+2y, 6x-8y

**Trinomial:** A polynomial with three terms is called a Trinomial.

Example :x+y+z, 2x-7y-6z.

##
Degree of a Polynomial

**Linear polynomial:** If the degree of the polynomial is 1 then we say that the degree of the polynomial is 1 and is called linear polynomial.

Example 3x-5 Here x has degree 1

**Quadratic polynomial:** If the degree of the polynomial is 2 then we say that the degree of the polynomial is 2 and is called quadratic polynomial.

Example 3x

^{2}+2x-5

**Cubic polynomial:** If the degree of the polynomial is 3 then we say that the degree of the polynomial is 3 and is called cubic polynomial.

Example : 4x

^{3}-3x

^{2}+6x-7

**Biquadratic polynomial:** If the degree of the polynomial is 4 then we say that the degree of the polynomial is 4 and is called biquadrayic polynomial.

Example : 4x

^{4}+7x

^{3}+5x

^{2}-6x-7

**Algebraic operations:**
Add 3x and 16x

3x+16x=19x

Add 6xy,5xy,-7xy

6xy+5xy-7xy=4xy

Add 3x+7y and 5x+6y

3x+7y+ 5x+6y

Now group the like terms here and then add up

3x+5x+7y+6y=8x+13y

**Multiplication:**
To find the product of two expressions ,multiply each term in the first expression separately with each tern of the second expression. Then combine the like terms if any thing is there to get the product.

**Multiply the following: **
*(*2x+3y

*)**(*2x+5y

*)*
First take the first term 2x and multiply with the second bracket and then take the second term with the sign and multiply with the second bracket.

2x

*(*2x+5y

*)*+3y

*(*2x+5y

*)*
4x

^{2}+10xy +6xy+15y

^{2}
4x

^{2}+16xy+15y

^{2}
Answer :4x

^{2}+16xy+15y

^{2}
Now we shall introduce some of the most important terms in the square of the polynomial

*(*a+b

*)*2=

*(*a+b

*)**(*a+b

*)*
= a

*(*a+b

*)*+b

*(*a+b

*)*
= a

^{2}+ab+ab+b

^{2}
=a

^{2}+2ab+b

^{2}
*(*a-b

*)*2=

*(*a-b

*)**(*a-b

*)*
=a

*(*a-b

*)*-b

*(*a-b

*)*
=a2-ab-ab+b

^{2}
= a2-2ab+b

^{2}
**Word Problems:**
1.John as 6 green chocolates and 5 mango chocolates , how many chocolates in total does he have

Answer: green chocolates be x and mango chocolates be y

Answer :So x+y =6+5=11

2. If sally has 200 bugs and sall has 300 bugs express this has an algebraic equation

Answer : we can express X variable has 200 bugs and y variable has 300 bugs the fore it gives us the result X+Y =500 bugs. This is an algebraic expression.

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