Factor completely: (2x-3)^(2)-(x+6)^(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 = (2x - 3) and b = (x + 6).Apply formula: Apply the difference of squares formula. Using the formula for the difference of squares, we can write: (2x - 3)^2 - (x + 6)^2 = (2x - 3 + x + 6)(2x - 3 - (x + 6))Simplify each factor: Simplify each factor. Now we simplify the expressions inside the parentheses: First factor: (2x - 3 + x + 6) = (3x + 3) Second factor: (2x - 3 - x - 6) = (x - 9)Write final factored form: Write the final factored form. The completely factored form of the expression is: (3x + 3)(x - 9)

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Factor completely:

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

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

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(2 x-3)^{2}-(x+6)^{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, $a = (2x - 3)$ and $b = (x + 6)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula for the difference of squares, we can write: $\newline$ $(2x - 3)^2 - (x + 6)^2 = (2x - 3 + x + 6)(2x - 3 - (x + 6))$
Simplify each factor: Simplify each factor. $\newline$ Now we simplify the expressions inside the parentheses: $\newline$ First factor: $(2x - 3 + x + 6) = (3x + 3)$ $\newline$ Second factor: $(2x - 3 - x - 6) = (x - 9)$
Write final factored form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(3x + 3)(x - 9)$