Basic Engineering Mathematics, Fifth Edition

62 Basic Engineering Mathematics

9.2.1 Addition and subtraction

Problem 1. Find the sum of 4x, 3 x,− 2 xand−x

4 x+ 3 x+− 2 x+−x= 4 x+ 3 x− 2 x−x

(Note that+×−=−)

= 4 x

Problem 2. Find the sum of 5x, 3 y,z,− 3 x,− 4 y

and 6z

5 x+ 3 y+z+− 3 x+− 4 y+ 6 z

= 5 x+ 3 y+z− 3 x− 4 y+ 6 z

= 5 x− 3 x+ 3 y− 4 y+z+ 6 z

= 2 x−y+ 7 z

Note that the order can be changed when terms are sep-

arated by+and−signs. Only similar terms can be

combined.

Problem 3. Simplify 4x^2 −x− 2 y+ 5 x+ 3 y

4 x^2 −x− 2 y+ 5 x+ 3 y= 4 x^2 + 5 x−x+ 3 y− 2 y

= 4 x^2 + 4 x+y

Problem 4. Simplify 3xy− 7 x+ 4 xy+ 2 x

3 xy− 7 x+ 4 xy+ 2 x= 3 xy+ 4 xy+ 2 x− 7 x

= 7 xy− 5 x

Now try the following Practice Exercise

PracticeExercise 35 Addition and

subtraction in algebra (answers on page 343)

1. Find the sum of 4a,− 2 a, 3 aand− 8 a.


2. Find the sum of 2a, 5 b,− 3 c,−a,− 3 band
   7 c.


3. Simplify 2x− 3 x^2 − 7 y+x+ 4 y− 2 y^2.


4. Simplify 5ab− 4 a+ab+a.


5. Simplify 2x− 3 y+ 5 z−x− 2 y+ 3 z+ 5 x.
   6. Simplify 3+x+ 5 x− 2 − 4 x.
   7. Addx− 2 y+3to3x+ 4 y−1.
   8. Subtracta− 2 bfrom 4a+ 3 b.
   9. Froma+b− 2 ctake 3a+ 2 b− 4 c.


6. Fromx^2 +xy−y^2 takexy− 2 x^2.

9.2.2 Multiplicationand division

Problem 5. Simplifybc×abc

bc×abc=a×b×b×c×c

=a×b^2 ×c^2

=ab^2 c^2

Problem 6. Simplify− 2 p×− 3 p

−×−=+hence,− 2 p×− 3 p= 6 p^2

Problem 7. Simplifyab×b^2 c×a

ab×b^2 c×a=a×a×b×b×b×c

=a^2 ×b^3 ×c

=a^2 b^3 c

Problem 8. Evaluate 3ab+ 4 bc−abcwhen

a= 3 ,b=2andc= 5

3 ab+ 4 bc−abc= 3 ×a×b+ 4 ×b×c−a×b×c

= 3 × 3 × 2 + 4 × 2 × 5 − 3 × 2 × 5

= 18 + 40 − 30

= 28

Problem 9. Determine the value of 5pq^2 r^3 ,given

thatp= 2 ,q=

2

5

andr= 2

1

2

5 pq^2 r^3 = 5 ×p×q^2 ×r^3

= 5 × 2 ×

(

2

5

) 2

×

(

2

1

2

) 3