Factor completely: (7x-10)^(2)-(x+1)^(2) Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The expression (7x-10)² - (x+1)² is a difference of two squares, which can be factored using the formula a² - b² = (a - b)(a + b).Identify 'a' and 'b': Identify 'a' and 'b' for the formula. In our case, 'a' is (7x-10) and 'b' is (x+1). We will apply these to the difference of squares formula.Apply formula: Apply the difference of squares formula. Using the formula from Step 1, we get: (7x-10)² - (x+1)² = [(7x-10) - (x+1)][(7x-10) + (x+1)]Expand factors: Expand the factors. Now we expand the factors: [(7x-10) - (x+1)] = (7x-10-x-1) = (6x-11) [(7x-10) + (x+1)] = (7x-10+x+1) = (8x-9)Write final form: Write the final factored form. The factored form of the expression is: (6x-11)(8x-9)

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Factor completely:

(7x-10)^(2)-(x+1)^(2)
Answer:

Factor completely: $\newline$ $(7 x-10)^{2}-(x+1)^{2}$ $\newline$ Answer:

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Algebra 1

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Q. Factor completely:

\newline

(7 x-10)^{2}-(x+1)^{2}

\newline

Answer:

Recognize as difference of squares: Recognize the expression as a difference of squares. The expression $(7x-10)^2 - (x+1)^2$ is a difference of two squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Identify 'a' and 'b': Identify 'a' and 'b' for the formula. $\newline$ In our case, 'a' is $(7x-10)$ and 'b' is $(x+1)$ . We will apply these to the difference of squares formula.
Apply formula: Apply the difference of squares formula. $\newline$ Using the formula from Step $1$ , we get: $\newline$ $(7x-10)^2 - (x+1)^2 = [(7x-10) - (x+1)][(7x-10) + (x+1)]$
Expand factors: Expand the factors. $\newline$ Now we expand the factors: $\newline$ [(7x-10) - (x+1)\] = \$(7x-10-x-1) = $(6x-11)$ $\newline$ [(7x-10) + (x+1)\] = \$(7x-10+x+1) = $(8x-9)$
Write final form: Write the final factored form. $\newline$ The factored form of the expression is: $\newline$ $(6x-11)(8x-9)$