2.1.H: Homework

Exercise 1

\(7x^2+5x^2\)

Answer

\(12x^2\)

Exercise 2

\(4a−9a\)

Answer

\(−5a\)

Exercise 3

\(−5b−17b\)

Answer

\(−22b\)

Exercise 4

\(2a^2+b^2−6a^2\)

Answer

\(−4a^2+b^2\)

Exercise 5

\(a^{2}b−4a−5ab^2\)

Answer

\(a^{2}b−4a−5ab^2\)

Exercise 6

Add: \(4a,\,−3b,\,−8a\)

Answer

\(−4a−3b\)

Exercise 7

\((5y^2+12y+4)+(6y^2−8y+7)\)

Answer

\(11y^2+4y+11\)

Exercise 8

\((8x^2−5x+2)+(3x^2+3)\)

Answer

\(11x^2−5x+5\)

Exercise 9

\((4m^2−6m−3)−(2m^2+m−7)\)

Answer

\(2m^2−7m+4\)

Exercise 10

\((12s^2−15s)−(s−9)\)

Answer

\(12s^2−16s+9\)

Exercise 11

Subtract \((7w^2−4w+2)\) from \((8w^2−w+6)\)

Answer

\(w^2+3w+4\)

Exercise 12

Find the sum of \((8a^3−8a)\) and \((a^2+6a+12)\)

Answer

\(8a^3+a^2−2a+12\)

Exercise 13

Find the difference of
\((c^2+4c−33)\) and
\((c^2−8c+12)\)

Answer

\(12c−45\)

Exercise 14

\((7m^2+mn−8n^2)+(3m^2+2mn)\)

Answer

\(10m^2+3mn−8n^2\)

Exercise 13

\((u^2−v^2)−(u^2−4uv−3v^2)\)

Answer

\(4uv+2v^2\)

Exercise 16

\((5y^2+12y+4)+(6y^2−8y+7)\)

Answer

\(11y^2+4y+11\)

Exercise 17

\(x+[4x+2(x+y)]\)

Answer

\(7x+2y\)

Exercise 18

\([2m+3(m+n)−2(m−n)+n]−2m\)

Answer

\(m+6n\)

Exercise 19

\(a−[2c−3(a+c)+a]\)

Answer

\(3a+c\)

Exercise 20

\(−{−[3x−(4y+x)]}\)

Answer

\(2x−4y\)

Exercise 21

A contractor is estimating the amount of gravel needed for a landscaping project. The total amount of gravel required can be represented by the expression:

where G represents the amount of gravel needed for the main area.

Simplify the expression by combining like terms.

Answer

\(\frac{35}{12}G\)

Exercise 22

The total capacitance, \(C_T\), in a series circuit with two capacitors \(C_1\) ann \(C_2\) is given by the formula

\(\frac{1}{C_T}=\frac{1}{C_1}+\frac{1}{C_2}\)

Simplify the right-hand side of this equation.

Answer

\(\frac{C_1+C_2}{C_1C_2}\)