Factor completely: (2x-3)^(2)-(x+1)^(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 = (2x-3) and b = (x+1) Difference of squares formula: a^2 - b^2 = (a + b)(a - b)Apply formula: Apply the difference of squares formula. Using the formula from Step 1, we can write the expression as: (2x-3 + x+1)(2x-3 - (x+1))Simplify terms: Simplify the terms inside the parentheses. Simplify the first set of parentheses: (2x-3 + x+1) = (3x - 2) Simplify the second set of parentheses: (2x-3 - x - 1) = (x - 4)Write final form: Write the final factored form. The completely factored form of the expression is: (3x - 2)(x - 4)

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Factor completely:

(2x-3)^(2)-(x+1)^(2)
Answer:

Factor completely: $\newline$ $(2 x-3)^{2}-(x+1)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(2 x-3)^{2}-(x+1)^{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. $\newline$ $a = (2x-3)$ and $b = (x+1)$ $\newline$ Difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula from Step $1$ , we can write the expression as: $\newline$ $(2x-3 + x+1)(2x-3 - (x+1))$
Simplify terms: Simplify the terms inside the parentheses. $\newline$ Simplify the first set of parentheses: $\newline$ $(2x-3 + x+1) = (3x - 2)$ $\newline$ Simplify the second set of parentheses: $\newline$ $(2x-3 - x - 1) = (x - 4)$
Write final form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(3x - 2)(x - 4)$