Questions: Multiplying Polynomials Cube the expression: 2x-3 Select the correct response: 8x^3-27 8x^3+36x^2+54x+27 8x^3-36x^2+54x-27 2x^3-27

Multiplying Polynomials Cube the expression: 2x-3 Select the correct response: 8x^3-27 8x^3+36x^2+54x+27 8x^3-36x^2+54x-27 2x^3-27
Transcript text: Multiplying Polynomials Cube the expression : $2 x-3$ Select the correct response: $8 x^{3}-27$ $8 x^{3}+36 x^{2}+54 x+27$ $8 x^{3}-36 x^{2}+54 x-27$ $2 x^{3}-27$
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Solution

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Cubing the expression \(2x - 3\).

Using the binomial expansion formula.

We apply the formula \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\) where \(a = 2x\) and \(b = 3\).

Calculating each term.

Calculating \(a^3 = (2x)^3 = 8x^3\), \(3a^2b = 3(2x)^2(3) = 36x^2\), \(3ab^2 = 3(2x)(3^2) = 54x\), and \(b^3 = 3^3 = 27\).

Combining the terms.

The expression simplifies to \(8x^3 - 36x^2 + 54x - 27\).

The final expression is \(\boxed{8x^3 - 36x^2 + 54x - 27}\).

The final expression for cubing \(2x - 3\) is \(\boxed{8x^3 - 36x^2 + 54x - 27}\).

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