Rewrite the expression as a product of four linear factors: (12x^(2)+11 x)^(2)-20(12x^(2)+11 x)+75 Answer:

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Rewrite the expression as a product of four linear factors:  (12x^(2)+11 x)^(2)-20(12x^(2)+11 x)+75 Answer:

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Identify Expression: Let's first identify the expression we need to factor: (12x^(2)+11x)^(2) - 20(12x^(2)+11x) + 75 This is a quadratic in form, where the ＂variable＂ is (12x^2+11x). We can use the factoring method for a quadratic expression, which is generally of the form a^2 - 2ab + b^2 = (a - b)^2.Denote Variable: Let's denote A = 12x^2 + 11x. Then our expression becomes: A^2 - 20A + 75 Now we need to find two numbers that multiply to 75 and add up to -20. These numbers are -5 and -15.Find Multiplying Numbers: We can now rewrite the expression as a squared binomial: A^2 - 20A + 75 = (A - 5)(A - 15) Remember that A = 12x^2 + 11x, so we substitute back in: (12x^2 + 11x - 5)(12x^2 + 11x - 15)Rewrite as Binomial: Now we need to factor each quadratic expression. We start with the first one: 12x^2 + 11x - 5 We look for two numbers that multiply to 12*(-5) = -60 and add up to 11. These numbers are 15 and -4.Factor First Quadratic: We can now factor the first quadratic: 12x^2 + 11x - 5 = (3x - 1)(4x + 5)Factor Second Quadratic: Next, we factor the second quadratic: 12x^2 + 11x - 15 We look for two numbers that multiply to 12*(-15) = -180 and add up to 11. These numbers are 20 and -9.Combine Factors: We can now factor the second quadratic: 12x^2 + 11x - 15 = (3x - 5)(4x + 3)Finally, we combine the factors of both quadratic expressions to express the original expression as a product of four linear factors: (3x - 1)(4x + 5)(3x - 5)(4x + 3)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(12 x^{2}+11 x\right)^{2}-20\left(12 x^{2}+11 x\right)+75$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(12x2+11x)2−20(12x2+11x)+75 \left(12 x^{2}+11 x\right)^{2}-20\left(12 x^{2}+11 x\right)+75 (12x2+11x)2−20(12x2+11x)+75\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(12 x^{2}+11 x\right)^{2}-20\left(12 x^{2}+11 x\right)+75$ $\newline$ Answer: