Chapter 12: Q. 12.64 (page 1205)

Use Pascal’s Triangle to expand ${(x + 1)}^{6}$

Short Answer

Expert verified

$x^{6} + 6 x^{5} + 15 x^{4} + 20 x^{3} + 15 x^{2} + 6 x + 1$

Step by step solution

. Given Information

We are given the expression : ${(x + 1)}^{6}$ and we need to solve this using the Pascal's triangle

. Pascal's triangle

First we need to expand the given expression by using the formula :

${(a + b)}^{n} =__a^{n} +__a^{n - 1} b^{1} +__a^{n - 1} b^{2} + . . . +__a^{1} b^{n - 1} +__b^{n}$

After this we find the co-efficient by using the Pascal's triangle , we count the number of expression obtained and then use that number as the row number of the triangle :

. Expanding the expression

We need to expand the given expression :

${(x + 1)}^{6} =__x^{6} +__x^{6 - 1} 1^{1} +__x^{6 - 2} 1^{2} +__x^{6 - 3} 1^{3} +__x^{6 - 4} 1^{4} +__x^{6 - 5} 1^{5} +__x^{6 - 6} 1^{6}$

${(x + 1)}^{6} =__x^{6} +__x^{5} +__x^{4} +__x^{3} +__x^{2} +__x +__1$

. Putting the co-efficient

We see that the number of expression obtained after expanding is six so we will take the co-efficient from the sixth row of the Pascal's triangle, so we will get :

$x^{6} + 6 x^{5} + 15 x^{4} + 20 x^{3} + 15 x^{2} + 6 x + 1$

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Use Pascal’s Triangle to expand ${(x + 1)}^{6}$

Short Answer

Step by step solution

. Given Information

. Pascal's triangle

. Expanding the expression

. Putting the co-efficient

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Use Pascal’s Triangle to expand(x+1)6

Short Answer

Step by step solution

. Given Information

. Pascal's triangle

. Expanding the expression

. Putting the co-efficient

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Use Pascal’s Triangle to expand ${(x + 1)}^{6}$