Question
Use Pascal triangle to expand (x + y)6
Hint:
Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n , where n can be any positive integer and x, y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement.
We are asked to find the binomial expansion of 6 (x + y)6 using Pascal’s formula.
The correct answer is: 6Cr
Step 1 of 1:
The Pascal’s triangle is given by:
From the triangle, the seventh line would give the coefficients of the expansion of the polynomial ( x + y)6 . Thus, we have:
.
.The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
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Use Pascal triangle to expand 
The answer cam also be found by expanding the formula of 5Cr .
Use Pascal triangle to expand
The answer cam also be found by expanding the formula of 5Cr .
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You could also get the value of 
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You could also get the value of from by just multiplying a ( x + y) with .
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This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
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This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
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We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
