What is 1/((x-y))(x^3-3x^2y+3xy^2-y^3) ?

The solution to 1/((x-y))(x^3-3x^2y+3xy^2-y^3) is (x-y)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/((x-y))(x^3-3x^2y+3xy^2-y^3)

simplify

\frac{1}{( x - y )} (x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3})

(x - y)^{2}

Solution steps

\frac{1}{x - y} (x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Apply rule:

1 \cdot a = a

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

= \frac{x ^{3} - 3 x ^{2} y + 3 x y ^{2} - y ^{3}}{x - y}

Apply cube of difference rule:

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

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

= \frac{( x - y ) ^{3}}{x - y}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - y)^{3} = (x - y) (x - y)^{2}

= \frac{( x - y ) ( x - y ) ^{2}}{x - y}

Cancel the common factor:

x - y

= (x - y)^{2}

- 4 x + 2 - x^{2} + 2 x - 5 + 3 x^{2}

5 + \frac{11}{12}

(4 x y)^{2} (4 x y)^{3}

- 4 \cdot 0

x \to \infty lim (\frac{x}{0})

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