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

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)

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

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1 answer
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Answer 1

Bot GPT 4-o mini answered
19 days ago

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**