Exercise 42 Page 26

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

(4y+3z)(4y-3z)^2

PowToProdTwoFac

a^2=a* a

(4y+3z)(4y-3z)(4y-3z)

Distr

Distribute (4y-3z)

(4y+3z) ( 4y(4y-3z)-3z(4y-3z) )

▼

Distribute 4y & -3z

Distr

Distribute 4y

(4y+3z) ( 16y^2-12yz-3z(4y-3z) )

Distr

Distribute -3z

(4y+3z) ( 16y^2-12yz-12yz+9z^2 )

SubTerm

Subtract term

(4y+3z) ( 16y^2-24yz+9z^2 )

Distr

Distribute ( 16y^2-24yz+9z^2 )

4y( 16y^2-24yz+9z^2 )+3z( 16y^2-24yz+9z^2 )

▼

Distribute 4y & 3z

Distr

Distribute 4y

64y^3-96y^2z+36yz^2+3z( 16y^2-24yz+9z^2 )

Distr

Distribute 3z

64y^3-96y^2z+36yz^2+48y^2z-72yz^2+27z^3

Finally, let's identify and combine like terms. 64y^3 - 96y^2z + 36yz^2 + 48y^2z - 72yz^2+ 27z^3 ⇕ 64y^3 - 48y^2z - 36yz^2+ 27z^3