Quantitative reasoning?

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Dencology

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how do you find the third therm in (x+3)*5?

ans 90x*3

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There is triangular rule for coefficient of power terms:
1 for (x+a)^1
1 2 1 for (x+a)^2
1 3 3 1 for (x+a)^3
1 4 6 4 1 for (x+a)^4
1 5 10 10 5 1 for (x+a)^5 =>
1 x^5 + 5 x^4 a^1 +10 x^3 a^2 + 10 x^2 a^3 +5 x^1 a^4 + 1 a^5
and it goes on with this pattern, considering the power of each term should be adds up to the biggest power. meaning when you have (x+3)^5, the biggest power is 5 and then we have
10 (3)^2 (x)^3=90 x^3
if you have a question feel free to ask
 
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