62 Basic Engineering Mathematics
9.2.1 Addition and subtraction
Problem 1. Find the sum of 4x, 3x, −2x and −x
4x + 3x + −2x + −x = 4x + 3x − 2x − x
(Note that + ×− = −)
= 4x
Problem 2. Find the sum of 5x, 3y, z, −3x, −4y
and 6z
5x+3y + z + −3x + −4y + 6z
= 5x + 3y + z − 3x − 4y + 6z
= 5x − 3x + 3y − 4y + z + 6z
= 2x − y + 7z
Note that the order can be changed when terms are separated by + and − signs. Only similar terms can be
combined.
Problem 3. Simplify 4x 2 − x − 2y + 5x + 3y
4x
2
− x − 2y + 5x + 3y = 4x
2
+ 5x − x + 3y − 2y
= 4x
2
+ 4x + y
Problem 4. Simplify 3x y − 7x + 4x y + 2x
3x y − 7x + 4x y + 2x = 3x y + 4x y + 2x − 7x
= 7xy − 5x
Now try the following Practice Exercise
Practice Exercise 35 Addition and
subtraction in algebra (answers on page 343)
1. Find the sum of 4a, −2a, 3a and −8a.
2. Find the sum of 2a, 5b, −3c, −a, −3b and
7c.
3. Simplify 2x − 3x 2 − 7y + x + 4y − 2y 2 .
4. Simplify 5ab − 4a + ab + a.
5. Simplify 2x − 3y + 5z − x − 2y + 3z + 5x.
6. Simplify 3 + x + 5x − 2 − 4x.
7. Add x − 2y + 3 to 3x + 4y − 1.
8. Subtract a − 2b from 4a + 3b.
9. From a + b − 2c take 3a + 2b − 4c.
10. From x
2
+ x y − y
2 take x y − 2x
2 .
9.2.2 Multiplication and division
Problem 5. Simplify bc × 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 = 6p
2
Problem 7. Simplify ab × 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 + 4bc − abc when
a = 3, b = 2 and c = 5
3ab + 4bc − 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 5 pq 2 r 3 , given
that p = 2, q =
2
5
and r = 2
1
2
5 pq
2 r
3
= 5 × p × q
2
× r
3
= 5 × 2 ×
2
5
2
×
2
1
2
3