Page 101 - Start Up Mathematics_7

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4. Find the terms which contain x and also find the coefficient of x :
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(a) 3 – x y (b) 3x yz + 5 (c) 3x y + 3xy 2 (d) 10xy + 20x y
5. Identify the terms and their factors in the following expressions:
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2 2
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(a) x + 2xy + y (b) 3x + 4y 2 (c) x y + 2xy + 4
6. Identify the like terms in the following expressions:
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(a) x , y , 2x , x , –x y (b) ab c, a bc, ab c , c ab, b ac
7. Rewrite and encircle the like terms in the following expressions:
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2 2
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(a) xy – 4x y, 8x , 2xy , –4xy (b) 7ab, 7a, 8b, –a b , –3ab, 6ba
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(c) 7pq, 3p q, –3pq , –6pq, –qp
Addition of Algebraic Expressions
Addition of algebraic expressions can be done by grouping the like terms and adding them.
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For example, (2x + 4x + 3x + 3) + (3x + x + 5) = (2x + 3x ) + (4x + x ) + 3x + (3 + 5)
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= 5x + 5x + 3x + 8
Subtraction of Algebraic Expression
Subtraction of an algebraic expression from a given expression can be done as follows:
Step 1: Since subtracting a term is same as adding its additive inverse, therefore first change the
sign (positive to negative or negative to positive) of each term in the expression to be
subtracted.
Step 2: Next, add the two expressions.
For example, (3x + 2y) – (2x – y) = (3x + 2y) + (–2x + y) = 3x + 2y – 2x + y
= (3x – 2x) + (2y + y) = x + 3y
Example 8: Simplify the expressions by combining the like terms:
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(a) 3x – 5 + 7x + 2 (b) (4y + 7y – 3) – (8y – y – 4)
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(c) p – (p – q) – q – (q – p) (d) a + b (4 – 7a) + a (3b – 1) – (3b – ab + 2a b)
Solution: (a) 3x – 5 + 7x + 2 = (3x + 7x) + (–5 + 2) = 10x – 3
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(b) (4y + 7y – 3) – (8y – y – 4) = 4y + 7y – 3 – 8y + y + 4
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= (4y + y ) + (7y – 8y) + (–3 + 4) = 5y – y + 1
(c) p – (p – q) – q – (q – p) = p – p + q – q – q + p
= (p – p + p) + (q – q – q) = p – q
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(d) a + b (4 – 7a) + a (3b – 1) – (3b – ab + 2a b)
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= a + 4b – 7ab + 3a b – a – 3b + ab – 2a b
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= (a – a ) + (4b – 3b ) + (–7ab + ab ) + (3a b – 2a b)
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= b – 6ab + a b
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