Name ______________________________________ Block _____________
MATH 1 – Combining Polynomials - Sec. 6.5
Two different methods of Multiplying Polynomials by Polynomials
FOIL = Firsts, Outers, Inners, Lasts
Box Method
(3x + 4)(2x – 7)
4-25-14
(3x + 4)(2x – 7)
(3x + 4)(2x – 7)
2x -7
3x 6x2 -21x
6x2 – 21x + 8x – 28
6x2 – 13x – 28
+4
8x
-28
Remember: -- You are multiplying __________________, and ___________ the exponents of like bases.
-- Do not forget the _________ in front of the number!
-- When combining _______ _________, remember to write in _______________ order!
Other helpful tips: Before you ________ like terms, _________ how many ________ you have to make
sure you didn’t miss anything! i.e. if you are asked to ____________ a BINOMIAL times a TRINOMIAL,
you should initially end up with 6 terms before CLT ( because 2 x 3 = 6)
Practice A – Multiply the following polynomials and write in simplest form.
1. (x – 4)(2x + 9)
2. (-3y – 4)(2y + 2)
4.
(6x – 3)(2x2 + 4x – 3)
5. (5y + 4) (8y – 12)
7.
(2x + 6)(-3x2 + x + 5)
8. (2m - 10) (2m – 5)
3.
(8 + w)(-10 – 3w)
6. (3p + 4) (2p 2 +4p– 9)
9. (p3 + 2p) (p2 + 3p – 4)
6d2
Practice B – Find the area of each.
1.
5x + 2
2x – 3
2.
3y3
5x 4
3.
4.
6y4
4g4 h3
Practice C – Find the perimeter or circumference.
1.
3x2 + 4
2.
5g– 3
4d2+2
find area of shaded region
3.
x2 – 1
2d2
5.
4.
4x 3
6x2
6x3
Practice D – Find the volume.
1.
2.
3.
8y
2y
5x + 5
3x
15y
4x
Practice E— Simplify each expression. Do not leave any negative exponents.
( x 2 y)( x 9 y 3 )
1.
6.
11.
(3x 4 ) 5
3x 5 y 3
3.
6 xy 2
 7 gh 4 (2 g 5 h  6 g 8 )
2.
7.
(2 xy6 ) 4 (5x 3 ) 2
(4x3 – 7x2 + 3x) – (x3 + 8x2 – 7x)
8. 5r4(-2r + 5r2)
12.
14 y 5 x 8
4.
2x5 y 4
5.
9. 3x( 3x4 – 2x)
10. -2y3 ( 5y2 + 9y)
(4x – 2x2)(7x – 9 + 8x2)
9 p 3 r (7 p 2  2 pr )
13. 9p3r(7p2 + 2pr)