Algebra | Chapter 3 | 8th Maths : Summary

**SUMMARY**

• When the
product of two algebraic expressions we follow,

Multiply
the signs of the terms,

Multiply
the corresponding co-efficients of the terms.

Multiply
the variable factors by using laws of exponents.

• For dividing
a polynomial by a monomial, divide each term of the polynomial by a monomial.

• Identity:
An identity is an equation is satisfied by any value that replaces its variables
(s).

(*a* + *b*)^{2}
=
*a* ^{2} +
2*ab* + *b*^{2}

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

(*a - b*)^{2} *a* ^{2} - 2*ab b*^{2}

(*a* + *b*)^{3}
=
*a* ^{3} +
3*a*^{2}*b* + 3*ab* ^{2} +
*b*^{3}

*a *^{2}* *−* b*^{2}* *=* *(* a *+* b*)(* a *−* b*)

(*a* − *b*)^{3}
=
*a* ^{3} −
3*a*^{2}*b* + 3*ab* ^{2} −
*b*^{3}

(* x *+* b *)(* x *+* b*)(* x *+* c*)* *=* x *^{3}* *+* *(* a *+* b *+* c*)*x *^{2}* *+* *(* ab *+* bc
*+* ca *)*x *+* abc*

**• Factorisation: **Expressing an algebraic expression as
the product of two or more** **expression
is called Factorisation.

• An equation
containing only one variable with its highest power as one is called a linear equation
in one variable.

• The value
which replaces a variable in an equation so as to make the two sides of the equation
equal is called a solution or root of the equation.

• Graphing
is just a visual method for showing relationships between numbers.

• The horizontal
line is named as XOX’, called the X-axis. The vertical line is named as YOY’, called
the Y-axis. Both the axes are called **coordinate axes**. The plane containing the* x *axis and the* y *axis is known as the coordinate plane or the **Cartesian plane**.

• A point
is denoted by a pair (a,b) of two numbers ‘a’ and ‘b’ listed in a specific order
in which ‘a’ represents the distance along the X-axis and ‘b’ represents the distance
along the Y axis. It is called an ordered pair (a,b).

• The coordinate
axes divide the plane of the graph into four regions called quadrants.

• The line
graph for the linear equation is called a **linear graph**.

** **

**ICT CORNER**

Through this activity you will know about the Algebra, operations on them and study their properties as well.

**Step-1** Open the Browser and type the URL given
below.

**Step-2** Click on any one of the link in the
items to know about the basics in algebra, exponents, polynomial, quadric equation
etc.

**Step-3** For example, click on the “Balance While
adding and subtracting”, link under the Basic menu. A new tab will open in the browser
where you can see the interactive game on adding and subtracting algebra.

**Step-4** Likewise you can learn all the concepts
in algebra.

Web
URL Algebra:

https://www.mathsisfun.com/algebra/index.html

*Pictures
are indicatives only.

*If
browser requires, allow Flash Player or Java Script to load the page.

**ICT CORNER**

Expected Outcome

**Step-1** Open the Browser type the URL Link given
below (or) Scan the QR Code. GeoGebra work book named “ALGEBRA” will open. Click
on the worksheet named “Point Plotting”.

**Step-2** In the given worksheet you can get new
point by clicking on “New point”.Enter the correct point in the input box and press
enter.

Browse
in the link

Algebra:

https://www.geogebra.org/m/fqxbd7rz#chapter/409574 or Scan the QR Code.

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