What is factor p^3q^3-p^2q^2-pq+1 ?

The solution to factor p^3q^3-p^2q^2-pq+1 is (pq-1)^2(pq+1)

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factor p^3q^3-p^2q^2-pq+1

factor

p^{3} q^{3} - p^{2} q^{2} - pq + 1

(pq - 1)^{2} (pq + 1)

Solution steps

p^{3} q^{3} - p^{2} q^{2} - pq + 1

= (p^{3} q^{3} - p^{2} q^{2}) + (- pq + 1)

Factor out

p^{2} q^{2}

from

p^{3} q^{3} - p^{2} q^{2} : p^{2} q^{2} (pq - 1)

Factor out

- 1

from

- pq + 1 : - (pq - 1)

= p^{2} q^{2} (pq - 1) - (pq - 1)

Factor out common term

(pq - 1) : (pq - 1) (p^{2} q^{2} - 1)

= (pq - 1) (p^{2} q^{2} - 1)

Factor

p^{2} q^{2} - 1 : (pq + 1) (pq - 1)

= (pq - 1) (pq + 1) (pq - 1)

Apply exponent rule:

aa = a^{2}

(pq - 1) (pq - 1) = (pq - 1)^{2}

= (pq - 1)^{2} (pq + 1)

36 \cdot \frac{5}{18}

x^{6} - 10 x^{4} y^{2} + 9 x^{2} y^{4}

\frac{1}{2} + \frac{5}{3}

(x^{2} + 8)^{2} - 8

What is factor p^3q^3-p^2q^2-pq+1 ?
The solution to factor p^3q^3-p^2q^2-pq+1 is (pq-1)^2(pq+1)