write a topic sentence for the following paragraph...
Osborn was twenty-three and a year out of college, a compact, buoyant mass of energy and high spirits. He seemed to be wholly unaffected by either the physical or mental hazards of mountaineering and had already, by many spectacular ascents in the Alps and the Rockies, won a reputation as the most skilled and audacious of younger American climbers. Nace was in his forties – lean, taciturn, introspective. An official of the Indian Civil Service, he had explored and climbed the Himalayas for twenty years. He had been a member of all five of the unsuccessful British expeditions to K3, and in his last attempt had attained to within 500 feet of the summit, the highest point which any man had reached on the unconquered giant. This had been the famous, tragic attempt in which his fellow climber and lifelong friend, Captain Furness, had slipped and fallen ten thousand feet to his death. Nace rarely mentioned his name, but on the steel head of his ice-ax were engraved the words: To Martin from John. If fate were to grant that the ax of any one of us should be planted upon the summit of K3, I hoped this would be the one.
Answers
Osborn was of high spirits because he seemed to be unaffected by any mental or physical hazards.
A topic sentence also states the point the writer wishes to make about that subject. Generally, the topic sentence appears at the beginning of the paragraph. It is often the paragraph's very first sentence. A paragraph's topic sentence must be general enough to express the paragraph's overall subject.
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An expression such as ` (a+b)(a−b) ‘ is not a problem so doesn’t have a solution. You can however pose a problem/question such as `How can I expand this?’ or `What is this when I expand the brackets?’.
It is also important to clarify what mathematical context you are working in. For example, if a,b are numbers they commute and then (a+b)(a−b)=a2−b2 , but if they are square matrices then they may not commute so (a+b)(a−b)=a2−ab+ba−b2 is the best you can say without further information.
Another thing to note is that for some purposes (a+b)(a−b) may be the best form for the expression, for example you might be interested in knowing when this is zero given you know a , so you need to be aware of the real goal of what you are doing