Factor completely. 25d^(8)-80d^(4)+64=

Question

Factor completely.  25d^(8)-80d^(4)+64=

Bytelearn · Accepted Answer

Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic equation in the form of a perfect square trinomial. Step Calculation: Coefficients are 25, -80, 64. Step Output: Coefficients: 25, -80, 64Recognize Perfect Square Trinomial: Step Title: Recognize the Perfect Square Trinomial Concise Step Description: Determine if the quadratic is a perfect square trinomial by checking if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms. Step Calculation: The square root of 25d^8 is 5d^4, and the square root of 64 is 8. The middle term, -80d^4, is twice the product of 5d^4 and 8, which is 2 * 5d^4 * 8 = 80d^4. Since the middle term is negative, we have -2 * 5d^4 * 8 = -80d^4. Step Output: The quadratic is a perfect square trinomial.Write Factored Form: Step Title: Write the Factored Form Concise Step Description: Write the factored form of the perfect square trinomial. Step Calculation: The factored form is (5d^4 - 8)^2. Step Output: Factored Form: (5d^4 - 8)^2

Factor completely. $\newline$ $25 d^{8}-80 d^{4}+64=$

Full solution

More problems from Factor polynomials

Related topics

Factor completely.\newline25d8−80d4+64= 25 d^{8}-80 d^{4}+64= 25d8−80d4+64=

Factor completely. $\newline$ $25 d^{8}-80 d^{4}+64=$