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Popular >

expand (x^4-1)/(x-1)

Solution

expand

\frac{x ^{4} - 1}{x - 1}

Solution

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

Solution steps

\frac{x ^{4} - 1}{x - 1}

Factor

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

= \frac{( x ^{2} + 1 ) ( x + 1 ) ( x - 1 )}{x - 1}

Cancel the common factor:

x - 1

= (x^{2} + 1) (x + 1)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = x^{2}, b = 1, c = x, d = 1

= x^{2} x + x^{2} \cdot 1 + 1 \cdot x + 1 \cdot 1

= x^{2} x + 1 \cdot x^{2} + 1 \cdot x + 1 \cdot 1

Simplify

x^{2} x + 1 \cdot x^{2} + 1 \cdot x + 1 \cdot 1 : x^{3} + x^{2} + x + 1

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

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Frequently Asked Questions (FAQ)

What is expand (x^4-1)/(x-1) ?
The solution to expand (x^4-1)/(x-1) is x^3+x^2+x+1