crealolobk

2021-12-29

How do you expand $(x-1)}^{3$ ?

veiga34

Beginner2021-12-30Added 32 answers

Explanation:

note that

$(x+a)}^{3}={x}^{3}+(a+a+a){x}^{2}+(a.a+a.a+a.a)x+{a}^{3$

${(x-1)}^{3}\to a=-1$

$\to {(x-1)}^{3}={x}^{3}+(-1-1-1){x}^{2}+(1+1+1)x+{(-1)}^{3}$

$={x}^{3}-3{x}^{2}+3x-1$

note that

Paul Mitchell

Beginner2021-12-31Added 40 answers

Use the Binomial Theorem.

$x}^{3}+3{x}^{2}\cdot -1+3x{(-1)}^{2}+{(-1)}^{3$

Simplify each term

Multiply -1 by 3.

$x}^{3}-3{x}^{2}+3x{(-1)}^{2}+{(-1)}^{3$

Raise -1 to the power of 2

$x}^{3}-3{x}^{2}+3x\cdot 1+{(-1)}^{3$

Multiply 3 by 1.

$x}^{3}-3{x}^{2}+3x+{(-1)}^{3$

Raise -1 to the power of 3

${x}^{3}-3{x}^{2}+3x-1$

Simplify each term

Multiply -1 by 3.

Raise -1 to the power of 2

Multiply 3 by 1.

Raise -1 to the power of 3

nick1337

Expert2022-01-08Added 777 answers

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