Factor completely: (3x+2)^(2)-(6x-7)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The given expression is in the form of a^2 - b^2, which is a difference of squares. A difference of squares can be factored into (a + b)(a - b). Here, a = (3x+2) and b = (6x-7).Apply formula: Apply the difference of squares formula. Using the formula (a + b)(a - b) to factor the expression, we get: ((3x+2) + (6x-7))((3x+2) - (6x-7))Simplify each factor: Simplify each factor. First factor: (3x+2) + (6x-7) = 3x + 2 + 6x - 7 = 9x - 5 Second factor: (3x+2) - (6x-7) = 3x + 2 - 6x + 7 = -3x + 9Write final form: Write the final factored form. The completely factored form of the expression is: (9x - 5)(-3x + 9)

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Factor completely:

(3x+2)^(2)-(6x-7)^(2)
Answer:

Factor completely: $\newline$ $(3 x+2)^{2}-(6 x-7)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(3 x+2)^{2}-(6 x-7)^{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 difference of squares can be factored into $(a + b)(a - b)$ . $\newline$ Here, $a = (3x+2)$ and $b = (6x-7)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula $(a + b)(a - b)$ to factor the expression, we get: $\newline$ $((3x+2) + (6x-7))((3x+2) - (6x-7))$
Simplify each factor: Simplify each factor. $\newline$ First factor: $(3x+2) + (6x-7) = 3x + 2 + 6x - 7 = 9x - 5$ $\newline$ Second factor: $(3x+2) - (6x-7) = 3x + 2 - 6x + 7 = -3x + 9$
Write final form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(9x - 5)(-3x + 9)$