Exploring Polynomial Function Multiplication

To convert them into standard form

To avoid mistakes in the final answer

To simplify the polynomials

To ensure the correct order of operations

FOIL method

Repeated multiplication

Distributive property

Factoring

12x^2

12x^4

7x^4

7x^2

Order

Opposite

Outside

Operation

2

4

3

5

Multiply the first terms

Multiply the outside terms

Multiply the last terms

Multiply the inside terms

x^3 + 9x^2 + 27x + 27

x^3 + 6x^2 + 18x + 27

x^3 + 6x^2 + 9x + 27

x^3 + 9x^2 + 18x + 27

16x^4 - 32x^3y + 24x^2y^2 - 8xy^3 - y^4

16x^4 - 32x^3y + 24x^2y^2 - 8xy^3 + y^4

16x^4 - 32x^3y + 24x^2y^2 + 8xy^3 - y^4

16x^4 - 32x^3y + 24x^2y^2 + 8xy^3 + y^4

Because x is multiplied by y

Because x comes before y alphabetically

Because y is a constant

Because x is a variable

Page 300, numbers 20 to 25 and 40 to 50

Page 310, numbers 25 to 29 and 46 to 58

Page 310, numbers 20 to 25 and 40 to 50

Page 300, numbers 25 to 29 and 46 to 58