Factor completely. 2x^(2)-50=

Identify common factor: Identify a common factor in the terms 2x^2 and -50. Both terms are divisible by 2. Factor out the common factor of 2. 2(x^2 - 25)Factor out common factor: Recognize that x^2 - 25 is a difference of squares. x^2 = x * x = (x)^2 25 = 5 * 5 = (5)^2 So, x^2 - 25 = (x)^2 - (5)^2Recognize difference of squares: Apply the difference of squares formula to factor x^2 - 25. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). (x)^2 - (5)^2 = (x - 5)(x + 5)Apply difference of squares formula: Combine the factored form of x^2 - 25 with the common factor we factored out in Step 1. 2(x - 5)(x + 5) This is the completely factored form of 2x^2 - 50.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

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2x^{2}-50=

Identify common factor: Identify a common factor in the terms $2x^2$ and $-50$ . $\newline$ Both terms are divisible by $2$ . $\newline$ Factor out the common factor of $2$ . $\newline$ $2(x^2 - 25)$
Factor out common factor: Recognize that $x^2 - 25$ is a difference of squares. $\newline$ $x^2 = x \times x = (x)^2$ $\newline$ $25 = 5 \times 5 = (5)^2$ $\newline$ So, $x^2 - 25 = (x)^2 - (5)^2$
Recognize difference of squares: Apply the difference of squares formula to factor $x^2 - 25$ . $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $(x)^2 - (5)^2 = (x - 5)(x + 5)$
Apply difference of squares formula: Combine the factored form of $x^2 - 25$ with the common factor we factored out in Step $1$ . $\newline$ $2(x - 5)(x + 5)$ $\newline$ This is the completely factored form of $2x^2 - 50$ .