Solve p^3(q - r)3 q^3(r - p)3 r^3(p - q)3

Question

Simplify the expression

- 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} + 27 p^{4} q^{5} r^{3} - 27 p^{4} q^{3} r^{5} + 27 p^{3} q^{4} r^{5} + 27 p^{5} q^{3} r^{4}

Evaluate

p^{3} (q - r) \times 3 q^{3} (r - p) \times 3 r^{3} (p - q) \times 3

Rewrite the expression in exponential form

p^{3} (q - r) \times 3^{3} q^{3} (r - p) r^{3} (p - q)

Multiply the terms

More Steps

27 p^{3} q^{3} r^{3} (q - r) (r - p) (p - q)

Multiply the terms

More Steps

(27 p^{3} q^{4} r^{3} - 27 p^{3} q^{3} r^{4}) (r - p) (p - q)

Multiply the terms

More Steps

(27 p^{3} q^{4} r^{4} - 27 p^{4} q^{4} r^{3} - 27 p^{3} q^{3} r^{5} + 27 p^{4} q^{3} r^{4}) (p - q)

Apply the distributive property

27 p^{3} q^{4} r^{4} p - 27 p^{3} q^{4} r^{4} q - 27 p^{4} q^{4} r^{3} p - (- 27 p^{4} q^{4} r^{3} q) - 27 p^{3} q^{3} r^{5} p - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{4} r^{4} q - 27 p^{4} q^{4} r^{3} p - (- 27 p^{4} q^{4} r^{3} q) - 27 p^{3} q^{3} r^{5} p - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{4} q^{4} r^{3} p - (- 27 p^{4} q^{4} r^{3} q) - 27 p^{3} q^{3} r^{5} p - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{4} r^{3} q) - 27 p^{3} q^{3} r^{5} p - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{5} r^{3}) - 27 p^{3} q^{3} r^{5} p - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{5} r^{3}) - 27 p^{4} q^{3} r^{5} - (- 27 p^{3} q^{3} r^{5} q) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{5} r^{3}) - 27 p^{4} q^{3} r^{5} - (- 27 p^{3} q^{4} r^{5}) + 27 p^{4} q^{3} r^{4} p - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{5} r^{3}) - 27 p^{4} q^{3} r^{5} - (- 27 p^{3} q^{4} r^{5}) + 27 p^{5} q^{3} r^{4} - 27 p^{4} q^{3} r^{4} q

Multiply the terms

More Steps

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} - (- 27 p^{4} q^{5} r^{3}) - 27 p^{4} q^{3} r^{5} - (- 27 p^{3} q^{4} r^{5}) + 27 p^{5} q^{3} r^{4} - 27 p^{4} q^{4} r^{4}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

27 p^{4} q^{4} r^{4} - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} + 27 p^{4} q^{5} r^{3} - 27 p^{4} q^{3} r^{5} + 27 p^{3} q^{4} r^{5} + 27 p^{5} q^{3} r^{4} - 27 p^{4} q^{4} r^{4}

The sum of two opposites equals 0

More Steps

0 - 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} + 27 p^{4} q^{5} r^{3} - 27 p^{4} q^{3} r^{5} + 27 p^{3} q^{4} r^{5} + 27 p^{5} q^{3} r^{4}

Solution

- 27 p^{3} q^{5} r^{4} - 27 p^{5} q^{4} r^{3} + 27 p^{4} q^{5} r^{3} - 27 p^{4} q^{3} r^{5} + 27 p^{3} q^{4} r^{5} + 27 p^{5} q^{3} r^{4}

Show Solution