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Factor completely: (x+9)(3x-1)-(x+9)^(2)(2x+3) Answer:

Factor completely:\newline(x+9)(3x−1)−(x+9)2(2x+3) (x+9)(3 x-1)-(x+9)^{2}(2 x+3) \newlineAnswer:

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Full solution

Q. Factor completely:\newline(x+9)(3x−1)−(x+9)2(2x+3) (x+9)(3 x-1)-(x+9)^{2}(2 x+3) \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms of the expression.\newlineThe common factor is (x+9)(x+9).
  2. Factor Out Common Factor: Factor out the common factor (x+9)(x+9) from both terms.(x+9)[(3x−1)−(x+9)(2x+3)](x+9)[(3x-1)-(x+9)(2x+3)]
  3. Distribute Negative Sign: Distribute the negative sign inside the second term.\newline(x+9)[(3x−1)−(x+9)(2x+3)]=(x+9)[(3x−1)−(2x2+3x+18x+27)](x+9)[(3x-1)-(x+9)(2x+3)] = (x+9)[(3x-1)-(2x^2+3x+18x+27)]
  4. Combine Like Terms: Combine like terms inside the brackets.\newline(x+9)[(3x−1)−(2x2+3x+18x+27)]=(x+9)[3x−1−2x2−3x−18x−27](x+9)[(3x-1)-(2x^2+3x+18x+27)] = (x+9)[3x-1-2x^2-3x-18x-27]
  5. Simplify Expression: Simplify the expression inside the brackets.\newline(x+9)[3x−1−2x2−3x−18x−27]=(x+9)[−2x2−18x+3x−1−27](x+9)[3x-1-2x^2-3x-18x-27] = (x+9)[-2x^2-18x+3x-1-27]
  6. Combine X Terms: Combine the xx terms inside the brackets.(x+9)[−2x2−18x+3x−1−27]=(x+9)[−2x2−15x−28](x+9)[-2x^2-18x+3x-1-27] = (x+9)[-2x^2-15x-28]
  7. Write Final Form: Write the final factored form.\newlineThe completely factored form is (x+9)(−2x2−15x−28)(x+9)(-2x^2-15x-28).

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