Topic Details (Notes format)

How to Use Pascal’s Triangle for Binomial Expansions

Subject: Mathematics

Book: Maths Mastery

Pascal’s triangle organizes binomial coefficients, where row n has C(n,k) for k=0..n. For example, row 4 is 1,4,6,4,1. In expansions like (x+y)⁴, the coefficients match those in row 4: x⁴+4x³y+6x²y²+4xy³+y⁴. Pascal’s triangle also applies to combinatorics, distributions, or probability logic (sums of binomial coefficients). Familiarity with it fosters mental expansions or quick coefficient retrieval in (a+b)^n expansions, streamlining binomial theorem tasks and combinatorial counting insights in advanced mathematics.

Practice Questions

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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What is the sum of all even numbers between 1 and 50?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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If the sum of three consecutive integers is 72, what are the integers?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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