Factor completely. 100-9x^(2)=

Determine the approach: Determine the approach to factor 100 - 9x^2. We can observe that the expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b).Identify in the form: Identify 100 - 9x^2 in the form of a^2 - b^2. 100 = 10 * 10 = 10^2 9x^2 = (3x) * (3x) = (3x)^2 So, 100 - 9x^2 = 10^2 - (3x)^2Apply the difference of squares formula: Apply the difference of squares formula to factor the expression. Using the formula a^2 - b^2 = (a - b)(a + b), we get: 10^2 - (3x)^2 = (10 - 3x)(10 + 3x)

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Factor completely. $\newline$ $100-9x^{2}=$

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

\newline

100-9x^{2}=

Determine the approach: Determine the approach to factor $100 - 9x^2$ . $\newline$ We can observe that the expression is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify in the form: Identify $100 - 9x^2$ in the form of $a^2 - b^2$ . $\newline$ $100 = 10 \times 10 = 10^2$ $\newline$ $9x^2 = (3x) \times (3x) = (3x)^2$ $\newline$ So, $100 - 9x^2 = 10^2 - (3x)^2$
Apply the difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $10^2 - (3x)^2 = (10 - 3x)(10 + 3x)$