Factor completely: (x-2)^(2)-(6x+5)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is in the form of a² - b², which is a difference of squares. a² - b² = (a - b)(a + b) Here, a = (x - 2) and b = (6x + 5).Apply formula: Apply the difference of squares formula. Using the formula from Step 1, we can write the expression as: ((x - 2) - (6x + 5))((x - 2) + (6x + 5))Simplify each factor: Simplify each factor. First factor: (x - 2) - (6x + 5) = x - 2 - 6x - 5 = -5x - 7 Second factor: (x - 2) + (6x + 5) = x - 2 + 6x + 5 = 7x + 3Write final factored form: Write the final factored form. The completely factored form of the expression is: (-5x - 7)(7x + 3)

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Factor completely:

(x-2)^(2)-(6x+5)^(2)
Answer:

Factor completely: $\newline$ $(x-2)^{2}-(6 x+5)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(x-2)^{2}-(6 x+5)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. $\newline$ The given expression is in the form of $a^2 - b^2$ , which is a difference of squares. $\newline$ $a^2 - b^2 = (a - b)(a + b)$ $\newline$ Here, $a = (x - 2)$ and $b = (6x + 5)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula from Step $1$ , we can write the expression as: $\newline$ $((x - 2) - (6x + 5))((x - 2) + (6x + 5))$
Simplify each factor: Simplify each factor. $\newline$ First factor: $(x - 2) - (6x + 5) = x - 2 - 6x - 5 = -5x - 7$ $\newline$ Second factor: $(x - 2) + (6x + 5) = x - 2 + 6x + 5 = 7x + 3$
Write final factored form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(-5x - 7)(7x + 3)$