Question

(5P3+2q2)*(4q4-10p3q2+25q6)

Answer 1

Если я правильно поняла условие то так
(5p³+2q²)*(4q⁴-10p³q²+25q^6)
20p³q⁴-50p^6q²+125p³q^6+8q^6-20p³q⁴+50q^8=-50p^6q²+125p³q^6+8q^6+50q^8

Answer 2

To simplify the given expression, let's expand it step by step:

1. Expand the first term (5P3 + 2q2): 5P3 + 2q2 = 5 * 4 * 3 / (3 * 2 * 1) + 2q2 = 5 * 4 + 2q2 = 20 + 2q2

2. Expand the second term (4q4 - 10p3q2 + 25q6): 4q4 - 10p3q2 + 25q6

3. Multiply the two expanded terms:

(20 + 2q2) * (4q4 - 10p3q2 + 25q6)

Now, to fully expand the expression, we need to apply the distributive property (FOIL method):

= 20 * 4q4 + 20 * (-10p3q2) + 20 * 25q6 + 2q2 * 4q4 + 2q2 * (-10p3q2) + 2q2 * 25q6

= 80q4 - 200p3q2 + 500q6 + 8q6 - 20p3q4 + 50q8

Finally, combine like terms:

= 80q4 + 8q6 - 200p3q2 - 20p3q4 + 500q6 + 50q8

The simplified expression is:

80q4 + 8q6 - 20p3q4 - 200p3q2 + 500q6 + 50q8