Factor completely: (x+9)^(2)-(5x-4)^(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 = (x+9) and b = (5x-4). 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: ((x+9) + (5x-4))((x+9) - (5x-4)).Simplify each binomial: Simplify each binomial. First binomial: (x+9) + (5x-4) = x + 9 + 5x - 4 = 6x + 5. Second binomial: (x+9) - (5x-4) = x + 9 - 5x + 4 = -4x + 13.Write final factored form: Write the final factored form. The completely factored form of the expression is: (6x + 5)(-4x + 13).

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Factor completely:

(x+9)^(2)-(5x-4)^(2)
Answer:

Factor completely: $\newline$ $(x+9)^{2}-(5 x-4)^{2}$ $\newline$ Answer:

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Grade 8

Powers with negative bases

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Q. Factor completely:

\newline

(x+9)^{2}-(5 x-4)^{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. $\newline$ $a = (x+9)$ and $b = (5x-4)$ . $\newline$ 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: $\newline$ $((x+9) + (5x-4))((x+9) - (5x-4))$ .
Simplify each binomial: Simplify each binomial. $\newline$ First binomial: $(x+9) + (5x-4) = x + 9 + 5x - 4 = 6x + 5$ . $\newline$ Second binomial: $(x+9) - (5x-4) = x + 9 - 5x + 4 = -4x + 13$ .
Write final factored form: Write the final factored form. $\newline$ The completely factored form of the expression is: $\newline$ $(6x + 5)(-4x + 13)$ .