Factor completely. 108-3x^(2)=

Identify common factor: Identify the common factor in the expression 108 - 3x^2. Both terms are divisible by 3.Factor out greatest common factor: Factor out the greatest common factor from the expression. 108 - 3x^2 = 3(36 - x^2)Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. 36 - x^2 can be written as (6)^2 - (x)^2, which is in the form a^2 - b^2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression inside the parentheses. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). So, 36 - x^2 = (6 - x)(6 + x).Combine factored expression: Combine the factored expression inside the parentheses with the common factor we factored out earlier. 3(36 - x^2) = 3(6 - x)(6 + x)

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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108-3x^{2}=

Identify common factor: Identify the common factor in the expression $108 - 3x^2$ . $\newline$ Both terms are divisible by $3$ .
Factor out greatest common factor: Factor out the greatest common factor from the expression. $108 - 3x^2 = 3(36 - x^2)$
Recognize difference of squares: Recognize that the expression inside the parentheses is a difference of squares. $36 - x^2$ can be written as $(6)^2 - (x)^2$ , which is in the form $a^2 - b^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression inside the parentheses. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ So, $36 - x^2 = (6 - x)(6 + x)$ .
Combine factored expression: Combine the factored expression inside the parentheses with the common factor we factored out earlier. $\newline$ $3(36 - x^2) = 3(6 - x)(6 + x)$