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Example 13: Identify the numerical coefficient of the terms (other than constant) and the
coefficient of x in terms containing x in the following algebraic expressions.
1
2
(a) –xy + 5xyz – 8 (b) x –3xy + 5yz (c) 4xy + 2yz – xz
2
Solution: Expressions Terms (other than Numerical Coefficient of x
constant term) Coefficient
2
(a) –xy + 5xyz – 8 –xy –1 –y 2
2
+ 5xyz + 5 5yz

(b) 1 x – 3xy + 5yz 1 x 1 1
2 2 2 2
–3xy –3 –3y
+5yz +5 –

(c) 4xy + 2yz – xz 4xy 4 4y
+2yz +2 –
–xz –1 –z

Quick Check
Write the numerical and algebraic coefficient of the following:
2
(a) –3m n (b) –4pqr
Numerical coefficient = _____________ Numerical coefficient = ____________
2
Coefficient of m = _________________ Coefficient of p = ____________
Coefficient of n = _______________ Coefficient of q = _____________
Coefficient of r = ___________
Coefficient of pq = ____________

Like and Unlike Terms

Terms having the same variable factors are called like terms.
For example: In algebraic expression 4xy – 3x + 5xy – 4, terms 2xy and 5xy have same algebraic
factors, i.e., xy.

So, 4xy and 5xy are like terms.
On the other hand, terms having different algebraic factors are called unlike terms.
2
For example: Terms 2xy and –3x have different algebraic factors as in 2xy, the algebraic factor is
2
2
xy and in –3x , the algebraic factors is –x .
Thus, 2xy and –3x are unlike terms.
2
Example 14: Identify the like and unlike terms in the following: Quick Check

2
2 2
2 2
2
2
7p, –2qr, 4x y , –20p, –7pq , 35x y , –9x y, 8pr, 4abc, 4ab, 9a b, 7abc Group the like terms together
Solution: Like Terms: 7p, –20p; 4x y , 35x y ; 4abc, 7abc from the following:
2 2
2 2
11x, 11, –24x, –24, –24y, 1, x,
2
2
2
Unlike Terms: –2qr , –7pq , –9x y, 8pr, 4ab, and 9a b 11y, y.
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