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Evaluate:

Question:
Evaluate:

(i) (38)2 − (37)2

(ii) (75)2 − (74)2

(iii) (92)2 − (91)2

(iv) (105)2 − (104)2

(v) (141)2 − (140)2

(vi) (218)2 − (217)2

Solution:

Given: $\left[(n+1)^{2}-n^{2}\right]=(n+1)+n$

(i) $(38)^{2}-(37)^{2}=38+37=75$

(ii) $(75)^{2}-(74)^{2}=75+74=149$

(iii) $(92)^{2}-(91)^{2}=92+91=183$

(iv) $(105)^{2}-(104)^{2}=105+104=209$

(v) $(141)^{2}-(140)^{2}=141+140=281$

(vi) $(218)^{2}-(217)^{2}=218+217=435$

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