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Factor completely: (10 x-7)^(2)-(3x+2)^(2) Answer:

Factor completely:\newline(10x−7)2−(3x+2)2 (10 x-7)^{2}-(3 x+2)^{2} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(10x−7)2−(3x+2)2 (10 x-7)^{2}-(3 x+2)^{2} \newlineAnswer:
  1. Recognize as difference of squares: Recognize the expression as a difference of squares. The expression (10x−7)2−(3x+2)2(10x - 7)^2 - (3x + 2)^2 is a difference of two squares, which can be factored using the formula a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b).
  2. Identify 'a' and 'b': Identify 'a' and 'b' in the formula.\newlineIn our case, 'a' is (10x−7)(10x - 7) and 'b' is (3x+2)(3x + 2).
  3. Apply formula: Apply the difference of squares formula.\newlineUsing the formula from Step 11, we get:\newline((10x−7)−(3x+2))((10x−7)+(3x+2))((10x - 7) - (3x + 2))((10x - 7) + (3x + 2))
  4. Simplify expressions: Simplify the expressions inside the parentheses.\newlineFirst, we simplify (10x−7)−(3x+2)(10x - 7) - (3x + 2), which gives us 10x−7−3x−2=7x−910x - 7 - 3x - 2 = 7x - 9.\newlineThen, we simplify (10x−7)+(3x+2)(10x - 7) + (3x + 2), which gives us 10x−7+3x+2=13x−510x - 7 + 3x + 2 = 13x - 5.
  5. Write final factored form: Write the final factored form.\newlineThe factored form of the expression is (7x−9)(13x−5)(7x - 9)(13x - 5).

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