What is factor 10p^2q^3+14p^3q^2-18p^4q^3-16p^5q^4 ?

The solution to factor 10p^2q^3+14p^3q^2-18p^4q^3-16p^5q^4 is 2p^2q^2(5q+7p-9p^2q-8p^3q^2)

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factor 10p^2q^3+14p^3q^2-18p^4q^3-16p^5q^4

factor

10 p^{2} q^{3} + 14 p^{3} q^{2} - 18 p^{4} q^{3} - 16 p^{5} q^{4}

2 p^{2} q^{2} (5 q + 7 p - 9 p^{2} q - 8 p^{3} q^{2})

Solution steps

10 p^{2} q^{3} + 14 p^{3} q^{2} - 18 p^{4} q^{3} - 16 p^{5} q^{4}

Apply exponent rule:

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

p^{2} q^{3} = p^{2} q^{2} q, p^{3} q^{2} = p^{2} p q^{2}, p^{4} q^{3} = p^{2} p^{2} q^{2} q, p^{5} q^{4} = p^{2} p^{3} q^{2} q^{2}

= 10 p^{2} q^{2} q + 14 p^{2} p q^{2} - 18 p^{2} p^{2} q^{2} q - 16 p^{2} p^{3} q^{2} q^{2}

Rewrite

- 16

8 \cdot 2

Rewrite

- 18

9 \cdot 2

= 5 \cdot 2 p^{2} q^{2} q + 7 \cdot 2 p^{2} p q^{2} + 9 \cdot 2 p^{2} p^{2} q^{2} q + 8 \cdot 2 p^{2} p^{3} q^{2} q^{2}

Factor out common term

2 p^{2} q^{2}

= 2 p^{2} q^{2} (5 q + 7 p - 9 p^{2} q - 8 p^{3} q^{2})

\frac{7}{24} + \frac{11}{30}

28 x^{2} + 20

4 \frac{2}{3} \div \frac{1}{2}

49 x^{2} - \frac{16}{25}

(- 4 y + 5 x) (- 3 x + 2 y)

What is factor 10p^2q^3+14p^3q^2-18p^4q^3-16p^5q^4 ?
The solution to factor 10p^2q^3+14p^3q^2-18p^4q^3-16p^5q^4 is 2p^2q^2(5q+7p-9p^2q-8p^3q^2)