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

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

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Full solution

Q. Factor completely:\newline(x−2)2−(10x+7)2 (x-2)^{2}-(10 x+7)^{2} \newlineAnswer:
  1. Recognize as difference of squares: Recognize the expression as a difference of squares. A difference of squares is an algebraic expression of the form a2−b2a^2 - b^2, which can be factored into (a−b)(a+b)(a - b)(a + b). Here, (x−2)2(x-2)^2 is our 'a2a^2' and (10x+7)2(10x+7)^2 is our 'b2b^2'.
  2. Apply formula: Apply the difference of squares formula.\newlineUsing the formula (a2−b2)=(a−b)(a+b)(a^2 - b^2) = (a - b)(a + b), we can write:\newline(x−2)2−(10x+7)2=[(x−2)−(10x+7)][(x−2)+(10x+7)](x-2)^2 - (10x+7)^2 = [(x-2) - (10x+7)][(x-2) + (10x+7)].
  3. Simplify expressions: Simplify the expressions inside the brackets.\newlineFirst bracket: (x−2)−(10x+7)=x−2−10x−7=−9x−9(x-2) - (10x+7) = x - 2 - 10x - 7 = -9x - 9.\newlineSecond bracket: (x−2)+(10x+7)=x−2+10x+7=11x+5(x-2) + (10x+7) = x - 2 + 10x + 7 = 11x + 5.
  4. Write factored form: Write the factored form using the simplified expressions.\newlineThe factored form of the expression is (−9x−9)(11x+5)(-9x - 9)(11x + 5).

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