Factor completely: (8x-1)^(2)-(5x-2)^(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 can be factored into (a + b)(a - b). Here, a = (8x - 1) and b = (5x - 2).Apply formula: Apply the difference of squares formula. Using the formula (a + b)(a - b) to factor the expression, we get: ((8x - 1) + (5x - 2))((8x - 1) - (5x - 2)).Simplify each part: Simplify each part of the factored expression. First part: (8x - 1) + (5x - 2) = 8x + 5x - 1 - 2 = 13x - 3. Second part: (8x - 1) - (5x - 2) = 8x - 5x - 1 + 2 = 3x + 1.Write final form: Write the final factored form. The factored form of the expression is (13x - 3)(3x + 1).

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Q. Factor completely:

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(8 x-1)^{2}-(5 x-2)^{2}

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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 can be factored into $(a + b)(a - b)$ . $\newline$ Here, $a = (8x - 1)$ and $b = (5x - 2)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula $(a + b)(a - b)$ to factor the expression, we get: $\newline$ $((8x - 1) + (5x - 2))((8x - 1) - (5x - 2))$ .
Simplify each part: Simplify each part of the factored expression. $\newline$ First part: $(8x - 1) + (5x - 2) = 8x + 5x - 1 - 2 = 13x - 3$ . $\newline$ Second part: $(8x - 1) - (5x - 2) = 8x - 5x - 1 + 2 = 3x + 1$ .
Write final form: Write the final factored form. $\newline$ The factored form of the expression is $(13x - 3)(3x + 1)$ .