Page 141 - ICSE Math 7

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Example 6: The sum of two numbers is –8p + 10pq – 5q . If one of the numbers is 6p + 12pq – 7q ,
find the other number.
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Solution: To get the other number, subtract 6p + 12pq – 7q from –8p + 10pq – 5q .
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– 8p + 10pq – 5q 2
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6p + 12pq – 7q 2
– – + (Changing the sign)
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– 14p – 2pq + 2q 2

EXERCISE 12.2

1. Add the following.
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(a) 6mn, 4mn, –3mn (b) 1 xyz, xyz, –2xy (c) 4a , 5a , –6b , 3b
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(d) 8ab, 4ab, –5ab (e) 3pq, 5pq, –9pq, 5p (f) 5x , –15y , –10x 2
2. Subtract the following.
(a) 4x from –9x (b) –5x from –12x + 5 (c) 2abc from 3 – 10abc
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(d) 3ab from 9a b – 3ab (e) 3p q – 3 from 9p – 9p q (f) a – b from a + b 2
3. Add the given algebraic expressions.
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(a) 2a – 3b + 5a, 4a + 2b – 6a (b) 3xy + y – x , 8xy + 2y
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(c) pq + p – q , 3q + 2pq – 5 (d) lm + ml + 30, mn + 4lm – 5ml
4. Simplify the following algebraic expressions.
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(a) xy + y – 3xy + 5y 2 (b) lmn + 3mn – 5lmn + 6nm
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(c) a + 5b – 20ab + 5a (d) pq + 2qr – 3pq – 6qr
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5. Find the difference between ab + 3bc + 2a – 5b and 5a – 6b + 10ab.
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6. What should be subtracted from 3xy + 5y – 2x + 10 to get 7y – 2xy + 12?
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7. Subtract 5pq + 5p + 5pq from the sum of 3pq + 2pq + 5 and –30pq – 12pq + 10.
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8. The sum of two algebraic expressions is ab + 5a b – 12b . If one of the algebraic expressions
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is a b + 2ab – ab , find the other.
9. A stick is divided into three parts of lengths (7x – 3y + 2z) cm, (5x – 4y + 3z) cm and (y – 3x + z) cm.
Find the original length of the stick.
10. The sides of a triangle are (x + y) cm, (3x + 5y) cm and (10x – 3y) cm. Find the perimeter of the
triangle.
Multiplication
For any two variables a and b, their product is a × b which is written as ab. For any three variables,
a, b and c, multiplication of variables follows the properties given below.
(a) ab = ba (b) a(bc) = (ab)c (c) a × 0 = 0 × a = 0
(d) a × 1 = 1 × a = a (e) a × (b + c) = (a × b) + (a × c) = ab + ac
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Also, if a is a variable and m, n are two integers, then x × x = x m+n .
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