Page 127 - Maths Skills - 7

Algebraic Expressions 125

6. Simplify the following:

(i) (3x – 3x) – (3x – 3x ) (ii) (9r + 5r + 11r) + (–2r + 9r – 8r )
3
4
2
4
3
2
(iii) (3v + 8v – 10v ) – (– 12v + 4 + 14v ) (iv) (– 9v – 84) + (– 2uv – 2u + v ) + (– v + 4uv)
3
2
5
2
2
2
3
5
2
2
(v) (4x + 7x y ) – (– 6x – 7x y – 4x) – (10x + 9x )
3 2
2
3 2
2
2
7. How much should a + 2b – 3c be increased to get 3a?
8. What should be taken away from p – q + 2pq + 10 to obtain –2p – 2q + 7pq + 10?
2
2
2
2
9. Subtract 2m – 7q + 5 from 4p + 2q and add your result to 7m – 3m + 9q – 1.
2
10. Subtract 2a b – 3b from 3a – 5ab + 2b and subtract your result from the sum of the two expressions
2
2
2
2
2
3ab + 5b – 2a b and a b + 5a – 3ab .
2
2
2
2
2
2
VALUE OF AN EXPRESSION
We have already learned to form an algebraic expression as per the given statements. In mathematics, we use and
apply many formulae for solving real-life problems and thus we need to practise the art of finding the value of an
algebraic expression. Let us see one example to understand it better.
We know that the perimeter of a rectangle is given by 2(l + b) where l = length, b = breadth of the rectangle.
Hence, l and b are the variables and if we need to find the value for l = 10 m and b = 3 m.
The perimeter = 2 (l + b) = 2 (10 + 3) = 2 × 13 = 26 m
Let us learn more through examples.
Let’s Attempt
Example 1: Find the values of the given algebraic expressions for x = 1 and y = – 1.
(i) 3 + 4xy (ii) –7y + 2x (iii) –19x y + 3xy + 4
2 2
2
2
Solution: (i) 3x + 4xy = 3 × 1 + 4 × 1 × (–1) (ii) –7y + 2x
2
2
2
= 3 – 4 = – 7 × (–1) + 2 × 1 = –1 = – 7 + 2 = – 5
2
(iii) –19x y + 3xy + 4
2 2
= – 19 × 1 × (–1) + 3 × (1) × (– 1) + 4
2
2
= – 19 – 3 + 4 = – 22 + 4 = – 18
Example 2: Find the value of each expression for corresponding values of variables:
(i) p + m; m = 1, p = 5 (ii) y + 9 – x; x = 1, y = 3
2
(iii) a – 5 – b; a = 10, b = 4 (iv) y – (z + z ); y = 10, z = 2
2
(v) p + 10 + m; m = 9, p = 3
3
Solution: (i) p + m for m = 1, p = 5 (ii) y + 9 – x for x = 1, y = 3
2
= 5 + 1 = 25 + 1 = 26 = 3 + 9 – 1 = 12 – 1 = 11
2
(iii) a – 5 – b for a = 10, b = 4 (iv) y – (z + z ) for y = 10, z = 2
2
= 10 – 5 – 4 = 1 = 10 – (2 + 2 )
2
(v) p + 10 + m for m = 9, p = 3 = 10 – (2 + 4) = 10 – 6 = 4
3
= 3 + 10 + 9
3
= 27 + 10 + 9 = 46