Factor completely. 81y^(2)-x^(2) Answer:

Recognize Squares: Step Title: Recognize the Difference of Squares Concise Step Description: Identify that the expression is a difference of two squares. Step Calculation: Recognize that 81y^2 is a perfect square (9y)^2 and x^2 is also a perfect square. Step Output: The expression can be written as (9y)^2 - x^2.Apply Formula: Step Title: Apply the Difference of Squares Formula Concise Step Description: Use the formula a^2 - b^2 = (a + b)(a - b) to factor the expression. Step Calculation: Factor the expression using the formula with a = 9y and b = x. Step Output: The factored form is (9y + x)(9y - x).

Home

Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Factor completely.

\newline

81 y^{2}-x^{2}

\newline

Answer:

Recognize Squares: Step Title: Recognize the Difference of Squares $\newline$ Concise Step Description: Identify that the expression is a difference of two squares. $\newline$ Step Calculation: Recognize that $81y^2$ is a perfect square $(9y)^2$ and $x^2$ is also a perfect square. $\newline$ Step Output: The expression can be written as $(9y)^2 - x^2$ .
Apply Formula: Step Title: Apply the Difference of Squares Formula $\newline$ Concise Step Description: Use the formula $a^2 - b^2 = (a + b)(a - b)$ to factor the expression. $\newline$ Step Calculation: Factor the expression using the formula with $a = 9y$ and $b = x$ . $\newline$ Step Output: The factored form is $(9y + x)(9y - x)$ .