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How Do You Expand \( (x-1)^3 \)?
You can Expand \( (x-1)^3 \) through formulas and simple multiplication method.
first of all, I am going to expand \( (x-1)^3 \) through the formula.
\( (a-b)^3 = a^3+3ab^2–3a^2b–b^3 \)
\( (x-1)^3 = x^3+3 \times x \times 1^2–3\times x^2 \times 1–1^3 \)
\( (x-1)^3 = x^3+3x – 3x^2 –1 \)
Now, I am going to expand \( (1-x)^3 \) through the Multiplication.
\( (x-1)^3 = (x-1)^2 (x-1) \)
\( (x-1)^3 = (x^2+1 – 2x) (x-1) \)
\( (x-1)^3 = x(x^2+1 – 2x) – 1 (x^2+1 – 2x) \)
\( (x-1)^3 = (x^3+x – 2x^2) – (x^2+1 – 2x) \)
\( (x-1)^3 = x^3+x – 2x^2 – x^2-1+ 2x \)
\( (x-1)^3 = x^3+3x – 3x^2 -1 \)
Expand Form of \( (x-1)^3 = x^3+3x – 3x^2 -1 \)