1. 9.7 MULTIPLYING POLYNOMIALS
You will learn:
to multiply two binomials
to multiply any two polynomials

2. Review: Multiplying Monomial by Polynomial
To multiply a monomial by a polynomial, you must distribute the monomial to each of the terms of the polynomial.
-3x(2x2 + 5x – 1)
-6x3
– 15x2
+ 3x

3. The next one…
10x3(2x2 – 7x + 8)
20x5
– 70x4
+ 80x3

4. What about this problem?
3a2b(5a2 + 3ab2 + 5b)
15a4b
+9a3b3
+ 15a2b2

5. Fractions too?
-5x3
+2x2y

6. Ex. 1) Multiplying a Binomial by a Polynomial
(3x – 4)(2x2 + 3x – 8) 3x
– 4
Distribute the first term
Now distribute the second term
– 24x
– 8x2
– 12x
+32
6x3
+9x2
Now combine like terms
6x3
+x2
– 36x
+32

7. Ex. 2) You can also use the table method
(5x2 + 6x)(3x3 + 2x – 9)
5x2
+ 6x
3x3
+ 2x
– 9
15x5
10x3
-45x2
18x4
12x2
-54x
15x5
+18x4
+10x3
– 33x2
– 54x

8. (x + 2)(3x – 8) (5x – 1)(-2x2 + 5x – 9) 3x2 – 2x – 16
Try It!
(x + 2)(3x – 8)
(5x – 1)(-2x2 + 5x – 9)
(3x + 2)(9x2 –12x + 4)
3x2 – 2x – 16
-10x3 + 27x2 – 50x + 9
27x3 – 18x2 – 12x + 8

9. Complete homework Page 539 (14-33)
Special Products tomorrow

10. Therefore: (x + 3)2 (x + 3) (x + 3) REMEMBER: x2 = x·x x2 +3x +3x +9 =
SPECIAL PRODUCTS
REMEMBER: x2 =
x·x
Therefore: (x + 3)2
(x + 3)
(x + 3) x2
+3x
+3x +9 = x2
+6x +9

11. x2 – 8x + 16 9x2 + 12x + 4 4x2 + 20xy + 25y2 (x – 4)2 (3x + 2)2
Try it!
(x – 4)2
(3x + 2)2
(2x + 5y)2
x2 – 8x + 16
9x2 + 12x + 4
4x2 + 20xy + 25y2

12. SPECIAL PRODUCTS
(x + 3)
(x - 3) x2
- 3x
+3x
- 9 = x2
+0x
- 9 x2
- 9

13. x2 –16 9x2 - 4 4x2 - 25y2 (x – 4)(x + 4) (3x + 2)(3x – 2)
Try it!
(x – 4)(x + 4)
(3x + 2)(3x – 2)
(2x + 5y)(2x – 5y)
x2 –16
9x2 - 4
4x2 - 25y2