What is expand q(200-200q-bq)^2 ?

The solution to expand q(200-200q-bq)^2 is -400q^2b+400q^3b+q^3b^2-80000q^2+40000q^3+40000q

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expand q(200-200q-bq)^2

expand

q (200 - 200 q - b q)^{2}

- 400 q^{2} b + 400 q^{3} b + q^{3} b^{2} - 80000 q^{2} + 40000 q^{3} + 40000 q

Solution steps

q (200 - 200 q - b q)^{2}

(200 - 200 q - b q)^{2} = - 400 q b + 400 q^{2} b + q^{2} b^{2} - 80000 q + 40000 q^{2} + 40000

= q (400 q^{2} b + q^{2} b^{2} + 40000 q^{2} - 400 q b - 80000 q + 40000)

Distribute parentheses

= q (- 400 q b) + q \cdot 400 q^{2} b + q q^{2} b^{2} + q (- 80000 q) + q \cdot 40000 q^{2} + q \cdot 40000

Apply minus-plus rules

+ (- a) = - a

= - 400 qq b + 400 q^{2} q b + q^{2} q b^{2} - 80000 qq + 40000 q^{2} q + 40000 q

Simplify

- 400 qq b + 400 q^{2} q b + q^{2} q b^{2} - 80000 qq + 40000 q^{2} q + 40000 q : - 400 q^{2} b + 400 q^{3} b + q^{3} b^{2} - 80000 q^{2} + 40000 q^{3} + 40000 q

= - 400 q^{2} b + 400 q^{3} b + q^{3} b^{2} - 80000 q^{2} + 40000 q^{3} + 40000 q

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What is expand q(200-200q-bq)^2 ?
The solution to expand q(200-200q-bq)^2 is -400q^2b+400q^3b+q^3b^2-80000q^2+40000q^3+40000q