When solving cube root equations, sometimes it is necessary to take extra steps when the radical is eliminated. If a binomial becomes cubed, it is necessary to multiply all three binomials together. In the case of (a−b)3 , or (a−b)(a−b)(a−b) , what is the result when the three binomials are multiplied?(1 point)

Question

Responses

a3−3a2b+3ab2−b3
a cubed minus 3 a squared b plus 3 a b squared minus b cubed

a3−3a2b−3ab2−b3
a cubed minus 3 a squared b minus 3 a b squared minus b cubed

a3−3a2b+3ab2+b3
a cubed minus 3 a squared b plus 3 a b squared plus b cubed

a3+3a2b+3ab2−b3

Answer 1

To multiply the binomial \((a - b)\) three times, we are calculating \((a - b)(a - b)(a - b)\) or \((a - b)^3\).

Using the binomial expansion formula for \((x - y)^3\): \[ (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3 \] we can substitute \(x\) with \(a\) and \(y\) with \(b\):

\[ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \]

Thus, the result when multiplying the three binomials \((a - b)(a - b)(a - b)\) is:

\[ a^3 - 3a^2b + 3ab^2 - b^3 \]

So, the correct answer from your provided options is:

a³ - 3a²b + 3ab² - b³