What is the answer to (x-1)(x-1)^3=(x-1)^4 ?

The answer to (x-1)(x-1)^3=(x-1)^4 is True for all x

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(x-1)(x-1)^3=(x-1)^4

(x - 1) (x - 1)^{3} = (x - 1)^{4}

True for all x

Solution steps

(x - 1) (x - 1)^{3} = (x - 1)^{4}

Simplify

(x - 1) (x - 1)^{3} : (x - 1)^{4}

(x - 1)^{4} = (x - 1)^{4}

Expand

(x - 1)^{4} : x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

Expand

(x - 1)^{4} : x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1 = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

Move

1

to the right side

x^{4} - 4 x^{3} + 6 x^{2} - 4 x = x^{4} - 4 x^{3} + 6 x^{2} - 4 x

Subtract

x^{4} - 4 x^{3} + 6 x^{2} - 4 x

from both sides

x^{4} - 4 x^{3} + 6 x^{2} - 4 x - (x^{4} - 4 x^{3} + 6 x^{2} - 4 x) = x^{4} - 4 x^{3} + 6 x^{2} - 4 x - (x^{4} - 4 x^{3} + 6 x^{2} - 4 x)

Simplify

0 = 0

Both sides are equal

True for all x

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What is the answer to (x-1)(x-1)^3=(x-1)^4 ?
The answer to (x-1)(x-1)^3=(x-1)^4 is True for all x
Solve for x: (x-1)(x-1)^3=(x-1)^4
The solution is True for all x