Question

Find the continued product: (5x + 2y) (5x – 2y) (25x2 + 4y?) (625x4 + 1674)​

Answer 1

The continued product is  $625x^8 + 1674625x^4 + 25y^4x^6100*1674$

To find the continued product of the given expressions, we can multiply them together and simplify the result.

The product of the first two expressions is:

$(5x + 2y)(5x - 2y) = (5x)^2 - (2y)^2 = 25x^2 - 4y^2$

Multiplying that with the third expression:

$(25x^2 - 4y^2)(25x^2 + 4y^2) = 25x^4 - 4y^4 + 4y^425x^2 = 625x^4 + 100y^425x^2$

Finally Multiplying that with the fourth expression:

$(625x^4 + 100y^425x^2)(625x^4 + 1674) = 625x^8 + 100y^425x^2625x^4 + 625x^41674 + 100y^425x^21674 = 625x^8 + 1674625x^4 + 25y^4x^6100*1674$

So, the continued product is:

$625x^8 + 1674625x^4 + 25y^4x^6100*1674$

• In mathematics, a continued product is a way of representing the product of an infinite series of numbers using an infinite nested product of fractions. It is a generalization of the concept of a continued fraction, which represents the quotient of an infinite series of numbers using an infinite nested fraction.
• In mathematics, a continued product is a way of representing the product of an infinite series of numbers using an infinite nested product of fractions. It is a generalization of the concept of a continued fraction, which represents the quotient of an infinite series of numbers using an infinite nested fraction.
• For example, the continued product of the sequence {a_n} is represented by the expression:    (a_1 * a_2 * a_3 * ...) / (1 * a_2 * a_3 * ...) * (1 * a_3 * a_4 * ...) * (1 * a_4 * a_5 * ...) * ...
• It is used in various branches of mathematics such as number theory and complex analysis

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