Factor completely: 16c^(4)-42c^(2)b^(3)-49b^(6) Answer:

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Factor completely:  16c^(4)-42c^(2)b^(3)-49b^(6) Answer:

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Identify Structure: Identify the structure of the polynomial and look for a common factoring strategy. The polynomial is a quadratic in terms of c^2, which suggests trying to factor it as if it were a quadratic equation.Recognize Form: Recognize that the polynomial is in the form of a quadratic trinomial ax^2 + bx + c. Here, we can consider c^2 as our variable x. So, we have a = 16, b = -42b^3, and c = -49b^6.Find Multiplying Numbers: Look for two numbers that multiply to ac (16 * -49b^6) and add to b (-42b^3). The numbers that satisfy this are -28b^3 and -14b^3 because (-28b^3)(-14b^3) = 392b^6 and -28b^3 - 14b^3 = -42b^3.Rewrite Middle Term: Rewrite the middle term of the polynomial using the two numbers found in the previous step: 16c^4 - 28b^3c^2 - 14b^3c^2 - 49b^6.Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms: (16c^4 - 28b^3c^2) - (14b^3c^2 + 49b^6).Factor Out Common Factors: Factor out the greatest common factor from each group. From the first group, we can factor out 4c^2, and from the second group, we can factor out 7b^3: 4c^2(4c^2 - 7b^3) - 7b^3(2c^2 + 7b^3).Recognize Common Factor: Notice that there is a common factor of (4c^2 - 7b^3) that can be factored out: (4c^2 - 7b^3)(4c^2 - 7b^3).Recognize Perfect Square: Recognize that (4c^2 - 7b^3)(4c^2 - 7b^3) is a perfect square and can be written as (4c^2 - 7b^3)^2.

Factor completely: $\newline$ $16 c^{4}-42 c^{2} b^{3}-49 b^{6}$ $\newline$ Answer:

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Factor completely:\newline16c4−42c2b3−49b6 16 c^{4}-42 c^{2} b^{3}-49 b^{6} 16c4−42c2b3−49b6\newlineAnswer:

Factor completely: $\newline$ $16 c^{4}-42 c^{2} b^{3}-49 b^{6}$ $\newline$ Answer: