Objective multiply two polynomials using the FOIL method and the distributive property.

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Presentation transcript:

Objective multiply two polynomials using the FOIL method and the distributive property.

There are two techniques you can use for multiplying polynomials. Distributive Property FOIL

1) Multiply. (2x + 3)(5x + 8) Using the distributive property, multiply 2x(5x + 8) + 3(5x + 8). 10x2 + 16x + 15x + 24 Combine like terms. 10x2 + 31x + 24 A shortcut of the distributive property is called the FOIL method.

The FOIL method is ONLY used when you multiply 2 binomials The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply. 2) Use the FOIL method to multiply the following binomials: (y + 3)(y + 7).

(y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial.

(y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial.

(y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial. y2 + 7y + 3y

y2 + 7y + 3y + 21 Combine like terms. y2 + 10y + 21 (y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y2 + 7y + 3y + 21 Combine like terms. y2 + 10y + 21

Remember, FOIL reminds you to multiply the: First terms Outer terms Inner terms Last terms

15x2 +6x -25x -10 3) Multiply (3x - 5)(5x + 2) First terms: Outer terms: Inner terms: Last terms: Combine like terms. 15x2 - 19x – 10 +6x -25x -10 You have 2 techniques. Pick the one you like the best!

21p2 -28p -6p +8 4) Multiply (7p - 2)(3p - 4) First terms: Outer terms: Inner terms: Last terms: Combine like terms. 21p2 – 34p + 8 -28p -6p +8

Multiply (y + 4)(y – 3) y2 + y – 12 y2 – y – 12 y2 + 7y – 12

Multiply (2a – 3b)(2a + 4b) 4a2 + 14ab – 12b2 4a2 – 14ab – 12b2 4a2 + 8ab – 6ba – 12b2 4a2 + 2ab – 12b2 4a2 – 2ab – 12b2

Group and combine like terms. 5) Multiply (2x - 5)(x2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property. 2x(x2 - 5x + 4) - 5(x2 - 5x + 4) 2x3 - 10x2 + 8x - 5x2 + 25x - 20 Group and combine like terms. 2x3 - 10x2 - 5x2 + 8x + 25x - 20 2x3 - 15x2 + 33x - 20

Multiply (2p + 1)(p2 – 3p + 4) 2p3 + 2p3 + p + 4 y2 – y – 12