Factor completely. 16n^(6)+40n^(3)+25=

Identify Structure: Identify the structure of the expression; it looks like a perfect square trinomial.Find Square Root: Find the square root of the first term, which is (4n^3)^2 = 16n^6.Check Middle Term: Find the square root of the last term, which is (5)^2 = 25.Write Factored Form: Check if the middle term is twice the product of the square roots of the first and last terms, which is 2 * 4n^3 * 5 = 40n^3.Write the factored form as a square of a binomial: (4n^3 + 5)^2.

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Factor completely. $\newline$ $16 n^{6}+40 n^{3}+25=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Factor completely.

\newline

16 n^{6}+40 n^{3}+25=

Identify Structure: Identify the structure of the expression; it looks like a perfect square trinomial.
Find Square Root: Find the square root of the first term, which is $(4n^3)^2 = 16n^6$ .
Check Middle Term: Find the square root of the last term, which is $(5)^2 = 25$ .
Write Factored Form: Check if the middle term is twice the product of the square roots of the first and last terms, which is $2 \times 4n^3 \times 5 = 40n^3$ .
Write Factored Form: Check if the middle term is twice the product of the square roots of the first and last terms, which is $2 \times 4n^3 \times 5 = 40n^3$ .Write the factored form as a square of a binomial: $(4n^3 + 5)^2$ .