Exercise 41 Page 26

125g^3+150g^2h+60gh^2+8h^3

Practice makes perfect

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.

(5g+2h)^3

a^3=a* a* a

(5g+2h)(5g+2h)(5g+2h)

Distr

Distribute (5g+2h)

(5g+2h) ( 5g(5g+2h)+2h(5g+2h) )

▼

Distribute 5g & 2h

Distr

Distribute 5g

(5g+2h) ( 25g^2+10gh+2h(5g+2h) )

Distr

Distribute 2h

(5g+2h) ( 25g^2+10gh+10gh+4h^2 )

AddTerms

Add terms

(5g+2h) ( 25g^2+20gh+4h^2 )

Distr

Distribute ( 25g^2+20gh+4h^2 )

5g( 25g^2+20gh+4h^2 )+2h( 25g^2+20gh+4h^2 )

▼

Distribute 5g & 2h

Distr

Distribute 5g

125g^3+100g^2h+20gh^2+2h( 25g^2+20gh+4h^2 )

Distr

Distribute 2h

125g^3+100g^2h+20gh^2+50gh^2+40h^2g+8h^3

Finally, let's identify and combine like terms. 125g^3 + 100g^2h + 20gh^2 + 50g^2h + 40gh^2+ 8h^3 ⇕ 125g^3 + 150g^2h + 60gh^2+ 8h^3

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Exercises p.25-27

Exercise 41 Page 26

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