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How do you simplify #n( n + 1) ^ { 2} ( 3n + 2)#?

Answer 1

Nathan Axel

#3n^4+8n^3+7n^2+2n#

Using the formula

#(a+b)^2=a^2+2ab+b^2# to get

#(n+1)^2=n^2+2n+1# and #n(n^2+2n+1)=n^3+2n^2+n# now we Need

#(n^3+2n^2+n)(3n+2)=#

#3n^4+6n^3+3n^2+2n^3+4n^2+2n# collecting like terms to get

#3n^4+8n^3+7n^2+2n#

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Answer 2

Eli Assouline

To simplify the expression (n(n + 1)^2(3n + 2)), expand the squared term first: ((n + 1)^2 = (n + 1)(n + 1) = n^2 + 2n + 1). Then, multiply the expanded term by (n) and the remaining term (3n + 2): (n(n^2 + 2n + 1)(3n + 2)). Distribute (n) into the parentheses: (n^3 + 2n^2 + n)(3n + 2)). Multiply each term in the first set of parentheses by each term in the second set of parentheses: (3n^4 + 6n^3 + 3n^2 + 2n^3 + 4n^2 + 2n). Combine like terms: (3n^4 + 8n^3 + 7n^2 + 2n). So, (n(n + 1)^2(3n + 2)) simplifies to (3n^4 + 8n^3 + 7n^2 + 2n).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.