Exercise 40 Page 26

We can find the product of this expression using polynomial identities. In this case, we have the cube of a binomial. We will first rewrite the cube as the product and then apply the Distributive Property.

(2r-3t)^3

a^3=a* a* a

(2r-3t)(2r-3t)(2r-3t)

Distr

Distribute (2r-3t)

(2r-3t) ( 2r(2r-3t)-3t(2r-3t) )

▼

Distribute 2r & -3t

Distr

Distribute 2r

(2r-3t) ( 4r^2-6rt-3t(2r-3t) )

Distr

Distribute -3t

(2r-3t) ( 4r^2-6rt-6rt+9t^2 )

SubTerm

Subtract term

(2r-3t) ( 4r^2-12rt+9t^2 )

Distr

Distribute ( 4r^2-12rt+9t^2 )

2r( 4r^2-12rt+9t^2 )-3t( 4r^2-12rt+9t^2 )

▼

Distribute 2r & - 3t

Distr

Distribute 2r

8r^3-24r^2t+18rt^2-3t( 4r^2-12rt+9t^2 )

Distr

Distribute - 3t

8r^3-24r^2t+18rt^2-12r^2t+36rt^2-27t^3

Finally, let's identify and combine like terms. 8r^3 - 24r^2t + 18rt^2 - 12r^2t + 36rt^2- 27t^3 ⇕ 8r^3 - 36r^2t + 54rt^2- 27t^3