Factor completely. 49m^(4)+140m^(2)+100=

Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic equation in terms of m^2. Step Calculation: Coefficients are 49, 140, and 100. Step Output: Coefficients: 49, 140, 100Recognize 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 square root of the first and last terms can be multiplied by 2 and equal the middle term. Step Calculation: The square root of 49m^4 is 7m^2, and the square root of 100 is 10. Multiply 7m^2 by 2 and then by 10 to see if it equals 140m^2. Step Output: 7m^2 * 2 * 10 = 140m^2Write Factored Form: Step Title: Write the Factored Form Concise Step Description: Write the factored form of the quadratic equation as a perfect square. Step Calculation: The factored form is (7m^2 + 10)^2. Step Output: Factored Form: (7m^2 + 10)^2

Home

Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Factor completely.

\newline

49 m^{4}+140 m^{2}+100=

Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic equation in terms of $m^2$ . $\newline$ Step Calculation: Coefficients are $49$ , $140$ , and $100$ . $\newline$ Step Output: Coefficients: $49$ , $140$ , $100$
Recognize Perfect Square Trinomial: Step Title: Recognize the Perfect Square Trinomial $\newline$ Concise Step Description: Determine if the quadratic is a perfect square trinomial by checking if the square root of the first and last terms can be multiplied by $2$ and equal the middle term. $\newline$ Step Calculation: The square root of $49m^4$ is $7m^2$ , and the square root of $100$ is $10$ . Multiply $7m^2$ by $2$ and then by $10$ to see if it equals $140m^2$ . $\newline$ Step Output: $7m^2 \times 2 \times 10 = 140m^2$
Write Factored Form: Step Title: Write the Factored Form $\newline$ Concise Step Description: Write the factored form of the quadratic equation as a perfect square. $\newline$ Step Calculation: The factored form is $(7m^2 + 10)^2$ . $\newline$ Step Output: Factored Form: $(7m^2 + 10)^2$