M5: Multiplying Polynomials

Question 1

(7x^2 + 8x + 2) (8x^2 + 6x + 5)

Answer 1

Use the box method to slove.
           7x^2      8x         2
          \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
8x^2 |  56x^4  | 64x^3 |  16x^2 |
6x     |  42x^3  | 48x^2 |  12x     |
5       |  35x^2  |   40x  |     10    |
          -----------------------------------
Add the like terms together 
56x^4 + 106x^3 + 99x^2 + 52x + 10

Question 2

(-3x^2y^4)(-6 x^3y)

Answer 2

18x^5y^5

Question 3

(x - 7)(x + 7)

Answer 3

x^2 - 49

Question 4

(3x + 2) (2x + 5)

Answer 4

6x^2 + 19x + 10

Question 5

(4x^2 - 4) (2x + 1)

Answer 5

8x^3 + 4x^2 - 8x - 4

Question 6

(4x + 2) (x - 2)

Answer 6

4x^2-6x-4

Question 7

(x^ 2 - 6) (x - 4)

Answer 7

x^3 -4x^2 -6x + 24

Question 8

(x ^2 + 8) (x - 5)

Answer 8

x^3 - 5x^2 + 8x - 40

Question 9

(x + 6) (x - 4)

Answer 9

x^2 + 2x − 24

Question 10

(x - 6)(x + 1)

Answer 10

x^2 − 5x − 6

Question 11

(5x^2 + 3y +5 )(y + 9)

Answer 11

5x^2 y+ 45x^2+ 3y^2+ 32y+ 45

Question 12

(x^2 + 11) (x + 6)

Answer 12

x^3 + 6x^2 + 11x + 66

Question 13

(x + 3) (x + 7)

Answer 13

x^2 + 10x + 21

Question 14

(x^2 + 9 )(x - 3)

Answer 14

x^3 − 3x^2 + 9x − 27

Question 15

(2x + 5)(x - 3)

Answer 15

2x^2 - x - 15

Question 16

(x - 3) (x^2 + 2x + 1)

Answer 16

x^3 − x^2 − 5x − 3

Question 17

(x + 4) (x^4 + x2 + 1)

Answer 17

x^5 + 4x^4 + x^3 + 4x^2 + x + 4

Question 18

(x^2 + x + 3)(x^3 - x^2 + 4)

Answer 18

x^5 + 2x^3 + x^2 + 4x + 12

Question 19

(x^2 + x)(x^3)

Answer 19

x^5 + x^4

Question 20

(x^2+2)(4x+20)

Answer 20

24x^3+8x+40

Question 21

(2x^2+2)(-3x+15)

Answer 21

-3x^3+30x^2-6x+30

Question 22

(x^2-5)(10x+20)

Answer 22

10x^3+20x^2-50x-100

Question 23

(-5x^2+1)(3x-2)

Answer 23

-15x^2+13x-2

Question 24

(-3x-2)(4x-5)

Answer 24

-12x^2+7x+10

Question 25

(6 x ^3)(-4 x ^4)

Answer 25

(6 x ^3)(-4 x ^4)
= (6 ∙ -4)(x ^3 ∙ x ^4)
= (6 ∙ -4)(x ^3 ^+ ^4)
= -24 x^7

Question 26

Multiplying Monomials

Answer 26

When multiplying Monomials, each term from one monomials must be multiplied by each term of the other monomials. Ex, a^m ∙ a ^n = a ^(m + n).