Identify Equation: Step Title: Identify the Equation Concise Step Description: Recognize the type of equation and identify its terms. Step Calculation: The equation is a quadratic in the form of b^2 - c^2, where b = 4b and c = 10. Step Output: Quadratic equation identified.Apply Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b), to factor the equation. Step Calculation: Applying the formula to 4b^2 - 100, we get (2b)^2 - 10^2 = (2b + 10)(2b - 10). Step Output: Factored form is (2b + 10)(2b - 10).Solve for b: Step Title: Solve for b Concise Step Description: Set each factor equal to zero and solve for b. Step Calculation: 1. 2b + 10 = 0 leads to 2b = -10, so b = -5. 2. 2b - 10 = 0 leads to 2b = 10, so b = 5. Step Output: Solutions for b are b = -5 and b = 5.

Algebra 2

Factor polynomials

Full solution

4

\quad 4 b^{2}-100=0

Identify Equation: Step Title: Identify the Equation $\newline$ Concise Step Description: Recognize the type of equation and identify its terms. $\newline$ Step Calculation: The equation is a quadratic in the form of $b^2 - c^2$ , where $b = 4b$ and $c = 10$ . $\newline$ Step Output: Quadratic equation identified.
Apply Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$ , to factor the equation. $\newline$ Step Calculation: Applying the formula to $4b^2 - 100$ , we get $(2b)^2 - 10^2 = (2b + 10)(2b - 10)$ . $\newline$ Step Output: Factored form is $(2b + 10)(2b - 10)$ .
Solve for b: Step Title: Solve for b $\newline$ Concise Step Description: Set each factor equal to zero and solve for b. $\newline$ Step Calculation: $\newline$ $1$ . $2b + 10 = 0$ leads to $2b = -10$ , so $b = -5$ . $\newline$ $2$ . $2b - 10 = 0$ leads to $2b = 10$ , so $b = 5$ . $\newline$ Step Output: Solutions for b are $b = -5$ and $b = 5$ .