Question: Find the HCF of the following expressions: (a+b)² -4ab, a³ -b³, and a² +ab -2b².

Solution:
Given,

1st expression: (a+b)² - 4ab
= (a² +2ab +b²) - 4ab
= (a² -2ab +b²)
= (a)² -2*a*b + (b)²
= (a -b)²
= (a-b)(a-b)

2nd expression: (a³ - b³)
= (a-b)(a² +ab +b²)

3rd expression: (a² +ab -2b²)
= a² +(2-1)ab -2b²
= a² +2ab -ab -2b²
= a (a +2b) -b (a +2b)
= (a -b)(a +2b)

Now,

Highest Common Factor (H.C.F.) = common factors only
= (a -b)

Related Notes and Solutions:

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