Hello friend, I’ve done few steps for 1st expression, but I can’t solve any further. Can u pls help?
1st expression:
= m3 - 8n3
= m3 - (2n)3
= (m - 2n)(m2 + 2mn + 4n2)
= (m - 2n)... ??
Hello David! If u feel u cann't simplify further, I recommend u to leave some space and move towards other expression. In this case, I left the 1st expression upto where u did, and started solving 2nd expression, and I ended up getting common factor.
Here is the full solution.
1st expression:
= m3 - 8n3
= m3 - (2n)3
= (m - 2n)(m2 + 2mn + 4n2)
2nd expression:
= 2m2 - 5mn + 2n2
= 2m2 - (4 + 1)mn + 2n2
= 2m2 - 4mn - mn + 2n2
= 2m(m - 2n) - n(m - 2n)
= (2m - n)(m - 2n)
3rd expression:
= 2m2 - 8n2
= 2(m2 - 4n2 )
= 2(m + 2n)(m - 2n)
From above, common factor is (m - 2n). So the HCF is (m - 2n).
Video explanation