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Factor completely: (8x-9)^(2)-(x+5)^(2) Answer:

Factor completely:\newline(8x−9)2−(x+5)2 (8 x-9)^{2}-(x+5)^{2} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(8x−9)2−(x+5)2 (8 x-9)^{2}-(x+5)^{2} \newlineAnswer:
  1. Recognize as difference of squares: Recognize the given expression as a difference of squares.\newlineThe expression (8x−9)2−(x+5)2(8x-9)^2 - (x+5)^2 is a difference of squares because it is in the form of a2−b2a^2 - b^2, where a=(8x−9)a = (8x-9) and b=(x+5)b = (x+5).
  2. Apply formula: Apply the difference of squares formula.\newlineThe difference of squares formula is a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b). We apply this to our expression where a=(8x−9)a = (8x-9) and b=(x+5)b = (x+5).
  3. Substitute values: Substitute the values of aa and bb into the formula.\newlineUsing the values of aa and bb, we get ((8x−9)−(x+5))((8x−9)+(x+5))((8x-9) - (x+5))((8x-9) + (x+5)).
  4. Simplify expressions: Simplify the expressions inside the parentheses.\newlineFirst, we simplify the left set of parentheses: (8x−9)−(x+5)=8x−9−x−5=7x−14(8x-9) - (x+5) = 8x - 9 - x - 5 = 7x - 14.\newlineThen, we simplify the right set of parentheses: (8x−9)+(x+5)=8x−9+x+5=9x−4(8x-9) + (x+5) = 8x - 9 + x + 5 = 9x - 4.
  5. Write final form: Write the final factored form.\newlineThe factored form of the expression is (7x−14)(9x−4)(7x - 14)(9x - 4).

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