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Differences of 3 * (2 + 5) and 3 * 2 + 5 For example, 3 * (2 + 5) = 21 3 * 2 + 5 = 11 These expression's solutions are different, but how do you distinguish these two expression on oral? Both seem "three times two plus 5", but of course the listener doesn't understand which one speaker means... ALSO, {-3(x+y)}^2 ... negative three x plus y raised to 2 ?? -3(x+y)^2 ... negative three x plus y raised to 2 ?? -3x+y^2... negative three x plus y raised to 2 ?? How do you distinguish these expressions on oral?? Please show me how to read such complex math expression... English is much more difficult than math...

Answers · 6

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I'll start off with the terminology we use (at least in the US). Brackets or parenthesis: ( ) Set brackets or (set) braces: { } Square brackets: [ ] For ^2, we say squared, ^3 cubed, ^4 to the fourth (power), ^5 to the fifth (power) {we don't tend to say "power" when we're reciting equations though} When we say equations orally, we will pause after saying the term or equation that has been bracketed to show the distinction of what the next operator is "operating on". I will indicate this verbal pause with "..." in the examples. So here's how I would say these when I teach: 3 * (2 + 5) = 21 => 3 times ...in parenthesis 2 plus 5 (close parenthesis)... equals 21 {in this case, the equation is simple enough that you don't need to say "close parenthesis"} 3 * 2 + 5 = 11 => 3 times 2 plus five equals 11 {-3(x+y)}^2 => set bracket negative/minus 3 times ...in parenthesis x plus y...close parenthesis, close bracket...(the whole thing) squared -3(x+y)^2 => negative/minus 3 times ...in parenthesis x plus y...close parenthesis squared -3x+y^2 => negative/minus 3 times x plus y squared
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If you absolutely had to do it without being able to write anything down, I think you'd say "open parenthesis," "close parenthesis," "open curly bracket," and "close curly bracket" for ( ) { and }, respectively. Everything else looks good once you include the parenthesis and brackets, but sometimes you'll hear, "to the second power," or just, "to the second." People would probably understand "raised to 2," but, "raised to the power of 2," might be easier for some to recognize. You could also leave 'raised' out and just put, "to the power of 2." Hope that helps. Good luck in your studies!
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In casual speech, it depends on intonation and rhythm. Usually you'd have a longer pause between things that need to be separated out, and say the rest as one word. You'd also raise your pitch before that longer pause. In formal speech, there are additional words you use to keep it clear. 3* (2 + 5) 3 times....... 2plus5...... equals21. times -> rising intonation (voice goes up), then a pause. 2 plus 5 would be said as one word and intonation would drop on the 5 (voice pitch goes down). 3 multiplied by the sum of 2 and 5. 3 * 2 + 5 3times2.......plus 5 equals 11 3times2 [one word, times has low intonation]then a short pause then plus 5 [five usually would have a rising intonation] multiply 3 by 2 and add 5. The others are all similar. {-3(x+y)}^2 ... negative three x plus y raised to 2 ?? negative3times... xplusy .......(all) squared. times has a rising intonation. xplusy is said as one word. squared - short, with a falling intonation. negative 3 times the sum of x + y, all squared -3(x+y)^2 ... negative three x plus y raised to 2 ?? it would be clearest to re-arrange this one ---- The square of XplusY multiplied by negative 3. -3x+y^2... negative three x plus y raised to 2 ?? negative3x + ysquared = the most natural reading of this one, but you can also say: negative 3 times x....... plus..... y squared.

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