Page 91 - Start Up Mathematics_8 (Non CCE)

2. Classify the following as monomials, binomials and trinomials:
2
2
2
2
(a) 2x + 3y (b) 7x + 4y + 7z (c) 425 (d) x y
3 2
2
2
2
(e) x + x y + 9x (f) x – 3 (g) a – 2a + 8b (h) a b c
3. Write two like terms to each of the following given terms.
2 4
2 3
(a) 8xy (b) 5x y (c) –4xy z
Addition of Algebraic Expressions
For adding algebraic expressions, collect different groups of like terms and find the sum in each group.
The sum of several like terms is also a like term whose coefficient is the sum of the coefficients of like terms.

Example 1: Add the following algebraic expressions:
(a) a – b + ab, b – c + bc, c – a + ac (NCERT)
2
2
2
2
2
2
(b) l + m , m + n , n + l , 2lm + 2mn + 2nl
Solution: (a) (a – b + ab) + (b – c + bc) + (c – a + ac)
= a – b + ab + b – c + bc + c – a + ac
= (a – a) + (–b + b) + (–c + c) + ab + bc + ac (Combining the like
= 0 + 0 + 0 + ab + bc + ac terms together)
= ab + bc + ac
2
2
2
2
2
2
(b) (l + m ) + (m + n ) + (n + l ) + (2lm + 2mn + 2nl)
2
2
2
2
2
2
= (l + l ) + (m + m ) + (n + n ) + 2lm + 2mn + 2nl (Combining the like
2
2
2
= 2l + 2m + 2n + 2lm + 2mn + 2nl terms together)
2
2
2
= 2(l + m + n + lm + mn + nl)
7 1 5 3 7 1 3 5
3
2
3
2
2
x
Example 2: Add: x - x + , x + x - + , x - x - 2
2 2 3 2 4 3 2 2
Ê 7 1 5ˆ Ê 3 7 1ˆ Ê 3 5 ˆ
2
3
2
2
3
+
Solution: Á 2 x - 2 x + 3¯ Ë 2 x + 4 x -+ 3¯ Ë 2 x - 2 x - 2 ˜
x
+
˜ Á
˜ Á
¯
Ë
Ê 7 3 3 ˆ Ê - 1 7 3 2 ˆ Ê 5 ˆ ÊÊ 5 1 ˆ
2
x +
= Á 2 x + 2 x ˜ ¯ + Á Ë 2 x + 4 x + 2 x ˜ Á x - 2 ¯ Ë 3 + - 2 (Combining the like
3
2
+-
˜
˜ Á
¯ Ë
¯
Ë
3
terms together)
2
2
2
10 Ê - 2x + 7x + 6x ˆ Ê - 2x - 5xˆ Ê 51 6ˆ
+-
3
= x + + Á ˜ + Á ˜
2 Á Ë 4 ˜ ¯ Ë 2 ¯ Ë 3 ¯
3
2
3
2
3
2
= 5x + 11 x - 7 x + 0 = 5x + 11 x - 7 x 7 x - 1 x + 5 ¸
4 2 4 2 2 2 3 Ô
Ô
3 7 1 ÔWriting like terms
2
3
Alternate Method: (Column Method) x + x + - x ˝ one below the other
4
Ô
Addition can also be carried out by using the column 2 3 3 5 Ô
2
method. First, write the first algebraic expression. + x - 2 - x Ô
Then write the other algebraic expression that is to 2 2 ˛
be added below the first algebraic expression, writing 10 x + 11 x + 0 - 7 x
2
3
like terms one below the other. 2 4 2
11 7
3
2
= 5x + x - x
4 2
83