For a4+ 4b4 + 5a2b2 + 5b4, LCM is 45a^4b^4 and HCF is a^2b^2
For a4+2a3b+a2b2-9b2, LCM is 8a^5b2 and HCF is a^2
LCM is the lowest common multiple
For a4+4b4 +(a2+b2)5b2
Expand the expression first
a4+ 4b4 + 5a2b2 + 5b4
a2 | a4+ 9b4+ 5a2b2
a2 | a2 + 9b4 + 5b2
b2 | 1 + 9b4 + 5b2
b2 | 1 + 9b2 + 5
5 | 1 + 9+ 1
9 | 1 + 1
To find the LCM, multiply all the factorials = a2 * a2 * b2 * b2 * 5 * 9 = 45 a4b4
HCF is known as the highest common factor
a2b2 | a4 + 9b4 + 5a2b2
| a2 + 9b2 + 5
The HCF = a2b2
For a4+2a3b+a2b2-9b2
Collect like terms
LCM
a2 | a4+ 2a3b+ a2b2- 9b2
a2 | a2 + 2ab + b2 - 9b2
2a | 1 + 2ab - 8b2
b | 1 + b- 4b2
4b | 1 + 1 -4b
| 1 + 1 -1
LCM = a2 * a2 * 2a* b * 4b = 8a^5b^2
The HCF
a2 |a4+ 2a3b+ a2b2- 9b2
| a2 + 2ab + b2 - 9b2
HCF = a^2
Therefore, the LCM and HCF of a4+4b4 +(a2+b2)5b2 is 45a^4b^4 and a^2b^2 respectively and that of a4+2a3b+a2b2-9b2 is 8a^5b62 and a^2 respectively
Learn more about LCM and HCF here:
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