Wednesday, August 17, 2011

Maths Level Test

Next week. Extraction, grouping and the rules(eg (a+b)^2=a^2+2ab+b^2)
Topics: Expansion
Factiorisation


Example: 1. 1^2-x^2=(1-x)(1+x)
2. 1-x^4=(1-x^2)(1+x^2)
=(1-x)(1+x)(1+x^2)
3. 1-x^8=(1)^2-{(x^4)}^2
=(1-x^4)(1+x^4)
=(1-x)(1+x)(1+x^2)(1+x^2)
4. 2-2x^4=2(1-x^4)
=2(1-x^2)(1+x^2)
=2(1-x)(1+x)(1+x^2)
5. (2-2x^4)^2=[2(1-x)(1+x)(1+x^2)]^2
=4(1-x)^2 (1+x)^2 (1+x^2)^2




Challenge Yourself W.S. 6
1. x^4-81=(x^2)^2 -(9)^2
=(x^2 -9)(x^2 +9)
=(x^2 -3^2)(x^2+9)
=(x-3)(x+3)9x^2+9)
2. m+n=11
m-n=23
----------
2m=34
m=11
17+n=11


n=-6
m=17

m+n=23
m-n=11
---------
2m=34
m=17
17+n=23




n=6
m=17




Discussion:

Ali has a problem:
(x^2)(y^2)+36-4x^2 -9y^2=???
=x^2 y^2 +36-9y^2
=x^2(y^2 -4)+9(4-y^2)
=x^2(y^2 -4)-9(y^2 -4)
=(y^2 -4)(x^2 -9)
=(y-2)(y+2)(x-3)(x+3)

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