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6. Add the following algebraic expressions.
(a) 30x + y – z, x – 30y + z and x + y – 30z (b) 11a + 13b + ab, b – 13a + 2ba and 3b + 11a – 3ab

3
4
2 3
2
(c) 3a b , –13a b , –7b a and –a b (d) 2p – 3p + p – 5p + 7, –3p – 7p – 3p – p – 12
2 3
3
4
2
2 3
3 2
2
2
2
2
2
(e) 25m n – 27mn + 18mn , 23m n – 25mn – 19mn and 22m n + 31mn – 34mn 2
7. Subtract the following algebraic expressions.
2
(a) 9x – 8y – 7z from 10x – 9y + 11z (b) 14a b – 7ab from 24a b + 8ab
2
2 2
2 2
2 2
2
2 2
2
2
(c) 2ab c + 4a b c – 5a bc from –10a b c + 4ab c + 2a bc 2
2
2
3
3
2
2
3
2 2
3
3
(d) 6n m – 5m – 2 from – 5m n + 2m + 1 (e) p + q + r – 3pqr from 8pqr – 5p + 7q – r 3
8. Subtract the sum of 35ab + 34bc + 4abc and 17bc + 3abc from the sum of 17bc + 40ac + 20abc and
33ab – 23abc.
Multiplication of Algebraic Expressions
There are multiple situations where we need to multiply algebraic expressions.
Suppose, you want to plant saplings in your garden in 6 rows with 12 saplings in each row, then
the total number of required saplings is 6 × 12 = 72. Similarly in algebra, if there were (3x – 7)
rows and you wanted to plant 4y saplings in each row, then the total number of saplings would
2
be (3x – 7) × 4y .
2
While finding the product of algebraic expressions, we should follow the steps given below:
Step 1: Multiply the signs of the terms as mentioned below.
Like Signs (+) × (+) = + (–) × (–) = +
Unlike Signs (+) × (–) = – (–) × (+) = –
Step 2: Multiply the corresponding coefficients of the terms.
Step 3: Multiplying the variable factors by using laws of exponents and powers.
Multiplication of a Monomial by a Monomial
When a monomial is multiplied with another monomial, it results into another monomial, where
the coefficients are multiplied and variables are multiplied together to give another monomial.
For example, (a) 4x × 3x = (4 × 3) × (x × x) = 12x 2 (b) 2x × 3y = (2 × 3) × (x × y) = 6xy
Thus we can say that,
Product of two monomials = Product of their numerical When we need to multiply three
coefficients × Product of or more monomials, usually we
their algebraic factors first multiply two monomials
and then multiply the resulting
Example 6: Find the product of the following pairs of monomial by the third monomial
monomials: and so on. But, we can also
2
(a) 15xy and 17yz 2 multiply them by getting the
products of all coefficients and all
(b) 4x y , 5y z and 2xz 3 algebraic factors.
2 3
2 4
2
2
2
Solution: (a) 15xy and 17yz = 15xy × 17yz 2
= (15 × 17) × (xy × yz ) = 255xy 2+1 2 3 2
2
z = 255xy z
2
2 4
3
2 3
3
2 4
2 3
2 3
2 4
3
(b) 4x y , 5y z and 2xz = 4x y × 5y z × 2xz = (4 × 5 × 2) × (x y × y z × xz )
3 5 7
= 40 × (x 2+1 × y 3+2 × z 4+3 ) = 40x y z
199 Algebraic Expressions