Expand: $(x - 1)^{3}$ .

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Solution

Use algebraic identity to simplify given expressions
Given expression: $(x - 1)^{3}$
Using the algebraic identity: ${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
${(x - 1)}^{3} = x^{3} - 1^{3} - 3 (x) (1) (x - 1)$
$= x^{3} - 1 - 3 x (x - 1) = x^{3} - 1 - 3 x^{2} + 3 x$
Therefore, ${(x - 1)}^{3} = x^{3} - 3 x^{2} + 3 x - 1$ .

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Expand: (x-1)3.

Use algebraic identity to simplify given expressionsGiven expression: (x-1)3Using the algebraic identity: (a–b)3=a3–b3–3ab(a–b)(x–1)3=x3–13–3(x)(1)(x–1) =x3–1–3x(x–1)=x3–1–3x2+3xTherefore, (x–1)3=x3–3x2+3x–1.

Expand: $(x - 1)^{3}$ .