Factor completely: (8x+1)^(2)-(x-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 = (x - 2).Apply formula: Apply the difference of squares formula. Using the formula (a + b)(a - b), we substitute a and b with (8x + 1) and (x - 2), respectively. So, the factored form is ((8x + 1) + (x - 2))((8x + 1) - (x - 2)).Simplify each binomial: Simplify each binomial. First binomial: (8x + 1) + (x - 2) = 8x + x + 1 - 2 = 9x - 1. Second binomial: (8x + 1) - (x - 2) = 8x - x + 1 + 2 = 7x + 3.Write final factored form: Write the final factored form. The expression is now factored completely as (9x - 1)(7x + 3).

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Q. Factor completely:

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

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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 $b = (x - 2)$ .
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula $(a + b)(a - b)$ , we substitute $a$ and $b$ with $(8x + 1)$ and $(x - 2)$ , respectively. $\newline$ So, the factored form is $((8x + 1) + (x - 2))((8x + 1) - (x - 2))$ .
Simplify each binomial: Simplify each binomial. $\newline$ First binomial: $(8x + 1) + (x - 2) = 8x + x + 1 - 2 = 9x - 1$ . $\newline$ Second binomial: $(8x + 1) - (x - 2) = 8x - x + 1 + 2 = 7x + 3$ .
Write final factored form: Write the final factored form. $\newline$ The expression is now factored completely as $(9x - 1)(7x + 3)$ .