Factor completely: (x-2)^(2)-(2x-7)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is a difference of two squares because it has the form a² - b², where a = (x-2) and b = (2x-7).Apply formula: Apply the difference of squares formula. The difference of squares formula is a² - b² = (a - b)(a + b). We will apply this formula to the given expression.Substitute values: Substitute the values of a and b into the formula. Using a = (x-2) and b = (2x-7), we get: ((x-2) - (2x-7))((x-2) + (2x-7))Simplify factors: Simplify each factor. First factor: (x-2) - (2x-7) = x - 2 - 2x + 7 = -x + 5 Second factor: (x-2) + (2x-7) = x - 2 + 2x - 7 = 3x - 9Write final form: Write the final factored form. The completely factored form of the expression is (-x + 5)(3x - 9).

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Factor completely:

(x-2)^(2)-(2x-7)^(2)
Answer:

Factor completely: $\newline$ $(x-2)^{2}-(2 x-7)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(x-2)^{2}-(2 x-7)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is a difference of two squares because it has the form $a^2 - b^2$ , where $a = (x-2)$ and $b = (2x-7)$ .
Apply formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . We will apply this formula to the given expression.
Substitute values: Substitute the values of $a$ and $b$ into the formula. $\newline$ Using $a = (x-2)$ and $b = (2x-7)$ , we get: $\newline$ $((x-2) - (2x-7))((x-2) + (2x-7))$
Simplify factors: Simplify each factor. $\newline$ First factor: $(x-2) - (2x-7) = x - 2 - 2x + 7 = -x + 5$ $\newline$ Second factor: $(x-2) + (2x-7) = x - 2 + 2x - 7 = 3x - 9$
Write final form: Write the final factored form. $\newline$ The completely factored form of the expression is $-x + 5$ ( $3$ x - $9$ ).