This document discusses multiplying polynomials. It provides examples of multiplying: 1) A monomial by a monomial, binomial, trinomial, and polynomial. 2) Applying polynomial multiplication to calculate the volume of a rectangular prism and cost of pencils. 3) A worksheet matching polynomial multiplication problems to their solutions. 4) An assignment with 5 polynomial multiplication problems.

1. PICTURE
ANALYSIS

2. Operations on
Polynomials:
Multiplication of
Polynomials

3. Focus Time!
1.Monomial to Monomial
Example:
2𝑥 3𝑥2
= 2 3 𝑥1+2
= 6𝑥3
(Literacy) Mono means one or single.
Monomial means single term.

4. Focus Time!
2. Monomial to Binomial
Example:
2𝑥 𝑥 + 3 = 2𝑥 𝑥 + 2𝑥 3 = 2𝑥2
+ 6𝑥
(Literacy) Bi means two.
Binomial means two terms.

5. Focus Time!
3. Monomial to Trinomial
Example:
2𝑥 3𝑥2
+ 5𝑥 + 1 = 2𝑥 3𝑥2
+ 2𝑥 5𝑥 + (2𝑥)(1)
(Literacy) Tri means three.
Trinomial means three terms.

6. Focus Time!
4. Monomial to Polynomial
Example:
2𝑥 𝑥3
+ 3𝑥2
+ 𝑥 − 5
= 2𝑥 𝑥3
+ 2𝑥 3𝑥2
+ 2𝑥 𝑥 − 2𝑥 5
= 2𝑥4
+ 6𝑥3
+ 2𝑥2
− 10
(Literacy) Poly means many.
Polynomial means many terms.

7. Application:
1. Find the volume of the rectangular prism whose
length, width, and height are (𝒙) meter, (𝟑𝒙) meter
and (5x) meter. (Hint:
𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒓𝒆𝒄𝒕𝒂𝒏𝒈𝒖𝒍𝒂𝒓 𝒑𝒓𝒊𝒔𝒎 = 𝒍 𝒙 𝒘 𝒙 𝒉)
2. If I bought (𝒙)pencils which cost (𝟓𝒙 − 𝟑) pesos
each, how much will I pay for it?

8. Worksheets Time!
Match Column A to Column B. Show the complete solution.
A. B.
__1. 𝟒𝒙 𝟔𝒙𝟐 − 𝒙 + 𝟐 (givers) 𝟑𝟓𝒙𝟐 + 𝟒𝟐𝒙
__2. 𝟔 𝟓𝒙 − 𝟓 (are) 𝟐𝟓𝒙 + 𝟐𝟓
__3. 𝟔𝒙(𝟔𝒙 − 𝟒) (The) 𝟐𝟒𝒙𝟑 − 𝟒𝒙𝟐 + 𝟖𝒙
__4. 𝟓(𝟓𝒙 − 𝟖) (the) 𝟒𝟎𝒙 − 𝟔𝟒
__5. 𝟖(𝟓𝒙 − 𝟖) (happiest) 𝟑𝟎𝒙 − 𝟑𝟎
__6. 𝟕𝒙(𝟓𝒙 + 𝟔) (people) 𝟑𝟔𝒙𝟐 − 𝟐𝟒𝒙
__7. 𝟐(𝟔𝒙 − 𝟑) (takers) 𝟐𝒙𝟑 + 𝟏𝟐𝒙𝟐 − 𝟖𝒙
__8. 𝟖𝒙(𝟔𝒙 + 𝟐) (the) 𝟒𝟖𝒙𝟐 + 𝟏𝟔𝒙
__9. (𝒙𝟐 + 𝟔𝒙 − 𝟒)(𝟐𝒙) (not) 𝟏𝟐𝒙 − 𝟔

9. Assignment:
Multiply the polynomials.
1.) (𝟐𝒙) (𝟑𝒙) (𝟐𝒙𝒚) (𝟓𝒙𝒚)
2. ) 𝒙 (𝟑 + 𝟓)
3.) −𝟐𝒙(𝟏𝟓𝒙 − 𝟏𝟕)
4.) 𝒙𝟐
(𝟑𝒙𝟒
+ 𝟑𝒙𝟑
− 𝟖𝒙𝟐
+ 𝟏𝟎𝒙 + 𝟐)
5.) 𝟕𝒙(𝟏𝟒𝒙𝟐
− 𝟗𝒙 + 𝟏𝟐)