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Factor completely: (x+4)^(2)-(9x+1)^(2) Answer:

Factor completely:\newline(x+4)2−(9x+1)2 (x+4)^{2}-(9 x+1)^{2} \newlineAnswer:

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Factor numerical expressions using the distributive propertyright chevron icon

Full solution

Q. Factor completely:\newline(x+4)2−(9x+1)2 (x+4)^{2}-(9 x+1)^{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+4)2(x+4)^2 is a2a^2 and (9x+1)2(9x+1)^2 is b2b^2.
  2. Apply formula: Apply the difference of squares formula.\newlineUsing the formula, we can write the expression as:\newline(x+4)+(9x+1))((x+4)−(9x+1))(x+4) + (9x+1))((x+4) - (9x+1))
  3. Simplify each factor: Simplify each factor.\newlineFirst factor: (x+4)+(9x+1)=x+4+9x+1=10x+5(x+4) + (9x+1) = x + 4 + 9x + 1 = 10x + 5\newlineSecond factor: (x+4)−(9x+1)=x+4−9x−1=−8x+3(x+4) - (9x+1) = x + 4 - 9x - 1 = -8x + 3
  4. Write final factored form: Write the final factored form.\newlineThe completely factored form of the expression is (10x+5)(−8x+3)(10x + 5)(-8x + 3).

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