Factor completely. 1-49x^(6) Answer:

Identify Expression: Step Title: Identify the Expression Concise Step Description: Recognize the type of expression and its components. Step Calculation: The expression is 1 - 49x^(6). Step Output: Expression components: 1, -49x^(6)Recognize Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Identify that the expression is a difference of squares. Step Calculation: A difference of squares is in the form a^2 - b^2, which can be factored into (a + b)(a - b). Here, 1 is the square of 1, and 49x^(6) is the square of (7x^(3)). Step Output: Difference of squares: 1^2 - (7x^(3))^2Factor Squares: Step Title: Factor the Difference of Squares Concise Step Description: Apply the difference of squares factoring formula. Step Calculation: Factoring 1 - 49x^(6) using the formula gives us (1 + 7x^(3))(1 - 7x^(3)). Step Output: Factored form: (1 + 7x^(3))(1 - 7x^(3))

Home

Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Factor completely.

\newline

1-49 x^{6}

\newline

Answer:

Identify Expression: Step Title: Identify the Expression $\newline$ Concise Step Description: Recognize the type of expression and its components. $\newline$ Step Calculation: The expression is $1 - 49x^{6}$ . $\newline$ Step Output: Expression components: $1$ , $-49x^{6}$
Recognize Squares: Step Title: Recognize the Difference of Squares $\newline$ Concise Step Description: Identify that the expression is a difference of squares. $\newline$ Step Calculation: A difference of squares is in the form $a^2 - b^2$ , which can be factored into $(a + b)(a - b)$ . Here, $1$ is the square of $1$ , and $49x^{6}$ is the square of $(7x^{3})$ . $\newline$ Step Output: Difference of squares: $1^2 - (7x^{3})^2$
Factor Squares: Step Title: Factor the Difference of Squares $\newline$ Concise Step Description: Apply the difference of squares factoring formula. $\newline$ Step Calculation: Factoring $1 - 49x^{6}$ using the formula gives us $(1 + 7x^{3})(1 - 7x^{3})$ . $\newline$ Step Output: Factored form: $(1 + 7x^{3})(1 - 7x^{3})$