Factor completely. 49q^(4)-4=

Identify Expression Type: Step Title: Identify the Type of Expression Concise Step Description: Recognize that the given expression is a difference of squares. Step Calculation: The expression 49q^(4) - 4 can be written as (7q^2)^2 - (2)^2, which is a difference of squares. Step Output: Expression is a difference of squares.Apply Difference of Squares Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b), to factor the expression. Step Calculation: Factoring 49q^(4) - 4 using the formula gives us (7q^2 + 2)(7q^2 - 2). Step Output: Factored form is (7q^2 + 2)(7q^2 - 2).

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Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Factor completely.

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49 q^{4}-4=

Identify Expression Type: Step Title: Identify the Type of Expression $\newline$ Concise Step Description: Recognize that the given expression is a difference of squares. $\newline$ Step Calculation: The expression $49q^{4} - 4$ can be written as $(7q^2)^2 - (2)^2$ , which is a difference of squares. $\newline$ Step Output: Expression is a difference of squares.
Apply Difference of Squares Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the difference of squares formula, which is $a^2 - b^2 = (a + b)(a - b)$ , to factor the expression. $\newline$ Step Calculation: Factoring $49q^{4} - 4$ using the formula gives us $(7q^2 + 2)(7q^2 - 2)$ . $\newline$ Step Output: Factored form is $(7q^2 + 2)(7q^2 - 2)$ .