1. Multiplying Polynomials
Turn in Extra Credit

2. Distributive Property
4y2z(y2 – 3z2)
Distribute (multiply)
4y2z•y2 – 4y2z•3z2
Multiply big #, add small #
4y2+2z – 4•3y2z1+2
4y4z – 12y2z3

3. TOO
1) -3s(s4 + 2s2t3) 2) 2pq(p2 – 3pq + 2q2) 3) 3(t – 2) – 5(t – 4)

4. Multiplying: Box Method
(2a – 5)(3a + 4) 3a 4 2a
6a2 8a
-20 -5
-15a
6a2 – 7a – 20

5. Multiplying: Box Method
(3x + 1)(x2 + 2x – 6) x2 2x -6 3x
3x3
6x2
-18x 1 x2 2x -6
3x3 + 7x2 – 16x – 6

6. TOO 4) (2n – 3)(n + 8) 5) (t – 3)(2t2 – t + 2)
6) (z2 – 2z + 4)(z + 3) 7) x2(x – 3)(x + 4)
Hint #7: Multiply first, then distribute

7. Special Cases Perfect Square Trinomial (1st)2 (2nd)2 Examples
(a ± b)2 = a2 ± 2ab + b2
(1st) (2nd)2
Examples
1) (3c + 4)2
(3c)2 + 2(12c) + 42
9c2 + 24c + 16
Multiply 1st • 2nd,
then double it
2) (p – 2q)2
p2 – 2(2pq) + (2q)2
p2 – 4pq + 4q2

8. Special Cases Difference of Squares (1st)2 – (2nd)2 Examples
(a + b)(a – b) = a2 – b2
(1st)2 – (2nd)2
Examples
1) (4k + 7)(4k – 7)
(4k)2 – 72
16k2 – 49
2) (5z + 6)(6 – 5z)
62 – (5z)2
36 – 25z2

9. YOU HAVE TO MEMORIZE THESE!
We are going to use them again when we do factoring later this chapter.
If you really can’t memorize and want to use the box, make sure that you have 2 parenthesis:
(a + b)2 = (a + b)(a + b)

10. TOO 8) (x + 3)2 9) (a – 2)2 10) (2y + 5)2 11) (3m + 6n)2
12) (k + 1)(k – 1) 13) (3r + 5)(3r – 5)
14) (4c + d)(4c – d) 15) (p2 – 2q2)(p2 + 2q2)

11. Homework Multiplying Polynomials Worksheet
Try and recognize the special cases and DO NOT use the box for them!

12. Answers to TOO problems
1) -3s5 – 6s3t3
2) 2p3q – 6p2q2 + 4pq3
3) -2t + 14
8) x2 + 6x + 9 9) a2 – 4a + 4
4y2 + 20y + 25
11) 9m2 + 36mn + 36n2
12) k2 – 1 13) 9r2 – 25
14) 16c2 – d2 15) p4 – 4q4
4) 2n2 + 13n – 24
5) 2t3 – 7t2 + 5t – 6
6) z3 + z2 – 2z + 12
7) x4 + x3 – 12x2