Page 124 - Maths Skills - 7

122 Maths

3. Identify monomials, binomials and trinomials in the following expressions:

−3 1
2
2
(i) 6a + 4b (ii) xy z (iii) 8a – 5b + 7c (iv) p + q – r
2
3
19 3
7
(v) 0.1a + 60b – 4c (vi) t – 16r (vii) 9zxy (viii) 4 + 7s – 6t
3
2
13
4. Identify all the like terms in the following expressions:
1
(i) xy , – 3xy, – 7x y, – 19y x, 4xy (ii) 8p, 7pq, 8q, –9pq, 3ab, p, 90q
2
2
2
3
1 −1
(iii) 2x y, – 13xy, – 15abc, – 5yx , yx, abc, 16 y
2
3
3
3 17
5. Write the algebraic expressions for the following statement:
(i) One fifth of n multiplied by difference of x and y.
(ii) Sum of cubes of p and q added to their sum.
(iii) Quotient of a and b subtracted from thrice of b
2
(iv) 4 more than twice of x.
(v) Total cost of x oranges at ` 45 per dozen and y mangoes at ` 5 per piece.

6. Find the degree of the following polynomials.
(i) x – 4x + 1 (ii) 3xy + 5 (iii) x + 3x y + 3xy + y 3
2
3
2
2
(iv) x – 5 (v) x + 5x + 7xy + 9 (vi) 7x y + xy + 10
7
2
4
6
ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS
Addition of Algebraic Expressions
To add the algebraic expressions, like terms are written together and then added. The sum of two or more like
terms is a like term having numerical coefficient equal to the sum of the numerical coefficients of all the like terms
being added and algebraic factor is the same as the algebraic factor of the given like terms.
For example, 4x + x + 2x – 3x = (4 + 1 + 2 – 3)x = 4x

Subtraction of Algebraic Expressions
The difference between two like terms is a like term whose numerical coefficient is equal to the difference
between the numerical coefficients of the two like terms and the algebraic factor is the same as the algebraic factor
of the given like terms.
For example, 6x – 8x = (6 – 8)x = – 2x.
We may use linear method or column method to add or subtract algebraic expressions as illustrated below:

Linear Method
In this method, we arrange all the terms of the algebraic expressions horizontally and then add or subtract their
like terms.

Column Method
In this method, each algebraic expression is written in a separate row such that like terms come one below the
other in a column and then we add or subtract the like terms.
Let us learn more through examples.