Chapter 12: Q. 12.61TI (page 1204)

Use Pascal’s Triangle to expand ${(x + y)}^{5}$

Short Answer

Expert verified

$x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{2} + 5 x y^{4} + y^{5}$

Step by step solution

. Given Information

We are given an expression $= {(x + y)}^{5}$ to solve it using the Pascal's triangle

. Pascal Triangle

The pascal triangle is :

We use this triangle to write the co-efficent of the expression and we explained the expression by using the formula : ${(a + b)}^{n} = a^{n} +___a^{n - 1} b^{1} +___a^{n - 2} b^{2} + . . . +___a^{1} b^{n - 1} + b^{n}$

. Expanding the expression

We expand the expression and we get :

${(x + y)}^{5} =__x^{5} y^{0} +__x^{5 - 1} y^{1} +__x^{5 - 2} y^{2} +__x^{5 - 3} y^{3} +__x^{5 - 4} y^{4} +__x^{5 - 5} y^{5}$

${(x + y)}^{5} =__x^{5} +__x^{4} y +__x^{3} y^{2} +__x^{2} y^{3} +__x y^{4} +__y^{5}$

. Adding the co-efficient from the Pascal's triangle

After expanding the expression we see that we get $6$ expression so we will take the sixth row's co-efficient of the pascal triangle. So we get :

$x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{2} + 5 x y^{4} + y^{5}$

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Use Pascal’s Triangle to expand ${(x + y)}^{5}$

Short Answer

Step by step solution

. Given Information

. Pascal Triangle

. Expanding the expression

. Adding the co-efficient from the Pascal's triangle

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Use Pascal’s Triangle to expand(x+y)5

Short Answer

Step by step solution

. Given Information

. Pascal Triangle

. Expanding the expression

. Adding the co-efficient from the Pascal's triangle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Calculus

Pure Maths

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use Pascal’s Triangle to expand ${(x + y)}^{5}$