Factor completely. 1-144x^(4) Answer:

Identify Form: Identify the form of the expression. The expression 1 - 144x^(4) is a difference of squares because it can be written as a^2 - b^2 where a = 1 and b^2 = 144x^(4).Find Square Root: Find the square root of b^2. The square root of 144x^(4) is 12x^2 because (12x^2)^2 = 144x^(4).Write as Difference: Write the expression as a difference of squares. The expression 1 - 144x^(4) can be written as (1)^2 - (12x^2)^2.Apply Formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). Here, a = 1 and b = 12x^2.Factor Expression: Factor the expression using the formula. Substitute a and b into the formula to get (1 + 12x^2)(1 - 12x^2).

Home

Math Problems

Algebra 1

Factor polynomials

Full solution

Q. Factor completely.

\newline

1-144 x^{4}

\newline

Answer:

Identify Form: Identify the form of the expression. $\newline$ The expression $1 - 144x^{4}$ is a difference of squares because it can be written as $a^2 - b^2$ where $a = 1$ and $b^2 = 144x^{4}$ .
Find Square Root: Find the square root of $b^2$ . The square root of $144x^{4}$ is $12x^2$ because $(12x^2)^2 = 144x^{4}$ .
Write as Difference: Write the expression as a difference of squares. $\newline$ The expression $1 - 144x^{4}$ can be written as $(1)^2 - (12x^2)^2$ .
Apply Formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . Here, $a = 1$ and $b = 12x^2$ .
Factor Expression: Factor the expression using the formula. $\newline$ Substitute $a$ and $b$ into the formula to get $(1 + 12x^2)(1 - 12x^2)$ .