Difference between revisions of "Factorisation"
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| − | = Hints for difficult problems = | + | # = Hints for difficult problems = |
Question : If x= and y= find | Question : If x= and y= find | ||
| Line 134: | Line 134: | ||
Step 8 : = | Step 8 : = | ||
| + | # =hints for dificult problem= | ||
| + | =====If x+y=a and xy=b then prove that (1+)+(1+) = | ||
| + | |||
| + | Steps for solution | ||
| + | |||
| + | step 1: * Understanding the problem first. | ||
| + | * Recalling the indentities | ||
| + | |||
| + | step 2 : * consider the condition and squaring on both side | ||
| + | * simplify to get the value | ||
| + | |||
| + | step 3: * consider LHS | ||
| + | * multiply the expression | ||
| + | * substitute the value | ||
| + | * simlpify the equqtion | ||
| + | |||
| + | |||
| + | solution for the problem | ||
| + | |||
| + | consider x+y=a | ||
| + | = | ||
| + | substitute x+y =a and xy=b | ||
| + | then we get | ||
| + | ------->(1) | ||
| + | consider xy=b squaring on both side | ||
| + | then we get =------->(2) | ||
| + | |||
| + | consider LHS= | ||
| + | =(1+)+(1+) | ||
| + | =1+ | ||
| + | = 1+ from eqn 1 & 2 | ||
| + | = | ||
| + | = | ||
| + | LHS = RHS============= | ||
= Project Ideas = | = Project Ideas = | ||
Revision as of 12:09, 15 February 2014
| Philosophy of Mathematics |
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Concept Map
Error: Mind Map file Factorisation of Polynomials.mm not found
Textbook
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Additional Information
Useful websites
- Maths is Fun. This website contains good worksheets for factorisation.
- Wolfram Mathworld. This website contains good simulations for math identities.
Reference Books
NCERT Books
Teaching Outlines
Concept #1 Monomial expressions
Learning objectives
To introduce expressions and the need and method of splitting
Notes for teachers
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Activity No #2 Demonstrate Binomial Cube
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept #
Learning objectives
Notes for teachers
Activity No #1 Geogebra
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
This is a Geogebra screenshot for identity.
This is a classroom demonstration of binomial cube. Show the children before you start the cubic identity.
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
- = Hints for difficult problems =
Question : If x= and y= find
Solution :
Analysing the given condition
Step 1 : = ()() => Using the formula : = ( )()
step 2 : = ( + )(-) => substitute the value of x and y
Step 3 : = x => take the L.C.M of the denominator , simplyfy using concept of addition and substaction of fraction
Step 4: = x simply the above using basic concepts of addition and substraction
Step 5 : = x
Step 6 := x => take common term 2 ( H.C.F)
Step 7 : = x
Step 8 : =
- =hints for dificult problem=
====If x+y=a and xy=b then prove that (1+)+(1+)
Steps for solution
step 1: * Understanding the problem first.
* Recalling the indentities
step 2 : * consider the condition and squaring on both side * simplify to get the value
step 3: * consider LHS * multiply the expression * substitute the value * simlpify the equqtion
solution for the problem
consider x+y=a = substitute x+y =a and xy=b
then we get
------->(1)
consider xy=b squaring on both side then we get =------->(2)
consider LHS= =(1+)+(1+) =1+ = 1+ from eqn 1 & 2 = =
LHS = RHS=============
Project Ideas
Math Fun
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