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Popular >

expand (x+1)^3(1-x)

Solution

expand

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

Solution

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

Solution steps

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

Expand

(x + 1)^{3} : x^{3} + 3 x^{2} + 3 x + 1

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

Distribute parentheses

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

Simplify

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

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

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(dy)/(dx)+y/x =2x^6y^2

\frac{d y}{d x} + \frac{y}{x} = 2 x^{6} y^{2}

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f (x) = x^{2} \cdot e^{- x^{2}}

f (x) = \frac{50}{x}

Frequently Asked Questions (FAQ)

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