Question

(9a2-1/2m3c)(9a2+1/2m2c)

Answer 1

(9a2-1/2m3c)(9a2+1/2m2c) = (18а-3/2см)•(18а+см) = 324а^2+18асм-27асм-3/2с^2м^2 = 324а^2-9асм-3/2с^2м^2

Answer 2

To multiply the expressions (9a^2 - (1/2)m^3c) and (9a^2 + (1/2)m^2c), you can use the distributive property (FOIL method). FOIL stands for First, Outer, Inner, Last, which is a method for multiplying two binomials. Here's how you can apply it to your expressions:

First: Multiply the first terms of both expressions. Outer: Multiply the outer terms of both expressions. Inner: Multiply the inner terms of both expressions. Last: Multiply the last terms of both expressions.

Here's the step-by-step calculation:

(9a^2 - (1/2)m^3c)(9a^2 + (1/2)m^2c)

First: (9a^2) * (9a^2) = 81a^4 Outer: (9a^2) * ((1/2)m^2c) = (9/2)a^2m^2c Inner: ((-1/2)m^3c) * (9a^2) = (-9/2)m^3a^2c Last: ((-1/2)m^3c) * ((1/2)m^2c) = (-1/4)m^5c^2

Now, combine these terms:

81a^4 + (9/2)a^2m^2c - (9/2)m^3a^2c - (1/4)m^5c^2

This is the result of multiplying the two expressions:

81a^4 + (9/2)a^2m^2c - (9/2)m^3a^2c - (1/4)m^5c^2