 # Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1.

## Presentation on theme: "Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1."— Presentation transcript:

Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 + 7y – 8y 2 – 1 ANSWER 2y 2 + 7y – 1

Monomial: 1 term Binomial: 2 terms Trinomial: 3 terms These are all polynomials Adding Polynomials: Combine the like terms Like Terms – Terms that have the same variables with the same exponents on them Combining Like Terms: Add the coefficients of each all like terms Ex. 3x + (-5x) = [3 + (-5)]x = -2x Add & Subtract Polynomials

Example: Rewrite Combine Like Terms

EXAMPLE 1 (3y 3 – 2y 2 – 7y) + (–4y 2 + 2y – 5) 3y 3 – 2y 2 – 4y 2 – 7y + 2y – 5 3y 3 – 6y 2 – 5y – 5 2. Add 3y 3 – 2y 2 – 7y and –4y 2 + 2y – 5 Gather like terms Combine like terms

EXAMPLE 2 (5z 2 – z + 3) – (4z 2 + 9z – 12 5z 2 – 4z 2 – z – 9z + 3 + 12 z 2 – 10z + 15 4. Subtract 4z 2 + 9z – 12 from from 5z 2 – z + 3 – 4z 2 – 9z + 12 Remember to distribute the – through the ( ) Gather like terms Combine like terms 5z 2 – z + 3

GUIDED PRACTICE for Examples 1 and 2 Find the sum 5. (t 2 – 6t + 2) + (5t 2 – t – 8) 6t 2 – 7t – 6 t 2 + 5t 2 – 6t – t + 2 – 8

GUIDED PRACTICE for Examples 1 and 2 6. (8d – 3 + 9d 3 ) – (d 3 – 13d 2 – 4) 8d 3 + 13d 2 + 8d + 1 Find the difference 8d – 3 + 9d 3 – d 3 + 13d 2 + 4 9d 3 – d 3 + 13d 2 + 8d – 3 + 4

There are three techniques you can use for multiplying polynomials. It’s all about how you write it… 1)Distributive Property-arrow multiplication 2)FOIL – also arrow multiplication! 3)Box Method I use arrow multiplication most often, you may use the method you like best.

Remember, FOIL reminds you to multiply the: F irst terms O uter terms I nner terms L ast terms

The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply. 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. y2y2

(y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial. y 2 + 7y

(y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial. y 2 + 7y + 3y

(y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y 2 + 7y + 3y + 21 Combine like terms. y 2 + 10y + 21

Multiply (2x - 5)(x 2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property. 2x(x 2 - 5x + 4) - 5(x 2 - 5x + 4) 2x 3 - 10x 2 + 8x - 5x 2 + 25x - 20 Group and combine like terms. 2x 3 - 10x 2 - 5x 2 + 8x + 25x - 20 2x 3 - 15x 2 + 33x - 20

x2x2 -5x+4 2x -5 Multiply (2x - 5)(x 2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property or box method. 2x 3 -5x 2 -10x 2 +25x +8x -20 Almost done! Go to the next slide!

x2x2 -5x+4 2x -5 Multiply (2x - 5)(x 2 - 5x + 4) Combine like terms! 2x 3 -5x 2 -10x 2 +25x +8x -20 2x 3 – 15x 2 + 33x - 20

Multiply Multiply 2 binomials Combine like terms Multiply the third binomial Combine like terms