McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Multiplying Polynomials
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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)
(5g+2h) ( 5g(5g+2h)+2h(5g+2h) )
â–Ľ
Distribute 5g & 2h
(5g+2h) ( 25g^2+10gh+2h(5g+2h) )
(5g+2h) ( 25g^2+10gh+10gh+4h^2 )
(5g+2h) ( 25g^2+20gh+4h^2 )
5g( 25g^2+20gh+4h^2 )+2h( 25g^2+20gh+4h^2 )
â–Ľ
Distribute 5g & 2h
125g^3+100g^2h+20gh^2+2h( 25g^2+20gh+4h^2 )
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