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Expand the expression to a polynomial in standard form:

left parenthesis, 3, x, plus, 1, right parenthesis, left parenthesis, 3, x, squared, minus, 10, x, minus, 3, right parenthesis
(3x+1)(3x
2
−10x−3)

1 answer

To expand the expression \((3x + 1)(3x^2 - 10x - 3)\), we will use the distributive property (often referred to as the FOIL method for binomials).

  1. Distribute \(3x\) across each term in the second polynomial: \[ 3x(3x^2) + 3x(-10x) + 3x(-3) = 9x^3 - 30x^2 - 9x \]

  2. Distribute \(1\) across each term in the second polynomial: \[ 1(3x^2) + 1(-10x) + 1(-3) = 3x^2 - 10x - 3 \]

  3. Combine all the expanded terms together: \[ 9x^3 - 30x^2 - 9x + 3x^2 - 10x - 3 \]

  4. Combine like terms:

    • The \(x^2\) terms: \(-30x^2 + 3x^2 = -27x^2\)
    • The \(x\) terms: \(-9x - 10x = -19x\)
    • The constant term: \(-3\)

Putting it all together, we find: \[ 9x^3 - 27x^2 - 19x - 3 \]

Thus, the expanded polynomial in standard form is: \[ \boxed{9x^3 - 27x^2 - 19x - 3} \]