Question
Use the binomial theorem to expand the expressions:
The correct answer is: (x^3+y^2 )^6=x^18+6x^15 y^2+15x^12 y^4+20x^9 y^6+15x^6 y^8+6x^3 y^10+y^12
ANSWER:
Hint:
The binomial expansion is
,
We are asked to find the expansion of using Binomial theorem.
Step 1 of 2:
The given expression is. Here, n=6, so we would have 6+1=7 terms in the expansion.
The values of
Step 2 of 2:
Substitute the values in the binomial equation to get the expansion of the expression;
Thus, the expansion of the expression is:
Note:
The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x+y)n, we would consider the (n+1)th row in the triangle.
Related Questions to study
Use the binomial theorem to expand the expressions:
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Use polynomial identities to factor each polynomial :
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
Use polynomial identities to factor each polynomial : 
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to factor each polynomial :
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions
Use polynomial identities to multiply each expression 
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Use polynomial identities to multiply each expression
Any expression of the form (a + b)2 can be expanded using the identity rather than using the conventional and time taking method of multiplying them, (a + b)(a + b)
Use polynomial identities to factor the polynomials or simplify the expressions :
Use polynomial identities to factor the polynomials or simplify the expressions :
Dakota said the third term of the expansions of 
is .Explain Dakota’s error and then correct the answer.
Dakota said the third term of the expansions of is .Explain Dakota’s error and then correct the answer.
Use polynomial identities to multiply each expression .
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Use polynomial identities to multiply each expression .
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
What number does C3 represent in the expansion 
? Explain.
What number does C3 represent in the expansion ? Explain.
Dakota said the third term of the expansions of .Explain Dakota’s error and then correct the answer.
You can use Both the Pascal’s triangle and binomial expansion to find the value of (x + y)n .
Dakota said the third term of the expansions of .Explain Dakota’s error and then correct the answer.
You can use Both the Pascal’s triangle and binomial expansion to find the value of (x + y)n .
