2.2.H: Homework

Exercise 1

\(2y·4y^3\)

Answer

\(8y^4\)

Exercise 2

\((-2xy^2z)·(7x^2z)\)

Answer

\(-14x^3y^2z^2\)

Exercise 3

\((7w^5y)·(8wy^2)\)

Answer

\(56w^6y^3\)

Exercise 4

\((−6c^{−3}d^9)(2c^4d^{−5})\)

Answer

\(−12cd^{4}\)

Exercise 5

4\((w+10)\)

Answer

4w+40

Exercise 6

−3(a+7)

Answer

−3a−21

Exercise 7

6r(4r+s)

Answer

\(24 r^{2}+6 r s\)

Exercise 8

(x−10)12x

Answer

\(12 x^{2}-120 x\)

Exercise 9

−9a(3a+5)

Answer

\(-27 a^{2}-45 a\)

Exercise 10

3\(\left(p^{2}+10 p+25\right)\)

Answer

\(3 p^{2}+30 p+75\)

Exercise 11

\(-8 x\left(x^{2}+2 x-15\right)\)

Answer

\(-8 x^{3}-16 x^{2}+120 x\)

Exercise 12

5\(q^{3}\left(q^{3}-2 q+6\right)\)

Answer

\(5 q^{6}-10 q^{4}+30 q^{3}\)

Exercise 13

\((2 m-9) m\)

Answer

\(2 m^{2}-9 m\)

Exercise 14

6\(x(4 x+y)\)

Answer

\(24 x^{2}+6 x y\)

Exercise 15

(w+5)(w+7)

Answer

\(w^{2}+12 w+35\)

Exercise 16

(11+p)(p−4)

Answer

\(p^{2}+7 p-44\)

Exercise 17

(6p+5)(p+1)

Answer

\(6 p^{2}+11 p+5\)

Exercise 18

(2t−9)(10t+1)

Answer

\(20 t^{2}-88 t-9\)

Exercise 19

(5x−y)(3x−6)

Answer

\(15 x^{2}-3 x y-30 x+6 y\)

Exercise 20

\(\left(x^{2}+3\right)(x+2)\)

Answer

\(x^{3}+2 x^{2}+3 x+6\)

Exercise 21

(5ab−1)(2ab+3)

Answer

\(10 a^{2} b^{2}+13 a b-3\)

Exercise 22

\((x+5)\left(x^{2}+4 x+3\right)\)

Answer

\(x^{3}+9 x^{2}+23 x+15\)

Exercise 23

\((y+8)\left(4 y^{2}+y-7\right)\)

Answer

\(4 y^{3}+33 y^{2}+y-56\)

Exercise 24

\(\left(w+3\right)^{2}\)

Answer

\(w^{2}+6 w+9\)

Exercise 25

\(\left(2x+y\right)^{2}\)

Answer

\(4x^{2}+4xy+y^2\)

Exercise 26

\(\left(2a+3b\right)^{2}\)

Answer

\(4a^{2}-12ab+9b^2\)

Exercise 27

\((7 p+10)(7 p-10)\)

Answer

\(49 p^{2}-100\)

Exercise 28

(4y+12z)(4y−12z)

Answer

\(16 y^{2}-144 z^{2}\)

Exercise 29

In calculating the work done by a variable force, the expression

is used, where \(F_1\)​ and \(F_2\) represent force measurements.

Simplify the expression.

Answer

\(\frac{1}{2}(F_2^2-F_1^2)\)

Exercise 30

The number of operations required to process a data file containing \(m\) records is modeled by the expression

\(3[m(m+4)+2m]\)

Simplify the expression.

Answer

\(3m^2+18m\)