Page 111 - Start Up Mathematics_8 (Non CCE)

7. The product of two factors with the same sign is positive and with different signs is negative.
n
m
8. If x is a variable and m, n are positive integers, then x ¥ x = x m + n .
9. The coefficient of the product of monomials is equal to the product of their coefficients.
10. The variable part in the product of monomials is equal to the product of the variable parts in the
given monomial.

11. If A, B, C and D are monomials, then
(a) A ¥ (B + C) = (A ¥ B) + (A ¥ C) (b) (B + C) ¥ A = (B ¥ A) + (C ¥ A)
(c) (A + B) ¥ (C + D) = A ¥ C + A ¥ D + B ¥ C + B ¥ D
12. An algebraic identity is a statement of equality between two algebraic expressions that is satisfied by
all the values of the variables.
13. Important identities:
2
2
2
2
2
(a) (p + q) = p + 2pq + q 2 (b) (p – q) = p – 2pq + q 2 (c) (p + q)(p – q) = p – q 2
14. Special products:
2
2
(a) (x + a)(x + b) = x + (a + b)x + ab (b) (x + a)(x – b) = x + (a – b)x – ab
2
2
(c) (x – a)(x + b) = x + (b – a)x – ab (d) (x – a)(x – b) = x – (a + b)x + ab
Review Exercises
Multiple ChoiCe Questions

2 2 2
2 2
2
1. In the algebraic expression 2x y – 3x y z + 3z , the coefficient of the middle term is:
(a) 2 (b) 3 (c) –3 (d) –2
2. (3x – 4y) – (2x – y) is equal to:
(a) x + 5y (b) x – 3y (c) 5x – y (d) x + 3y
2 3
3 2
3. The product (2xy z ) ¥ (6x y z) is equal to:
4 3 5
3 3 4
4 4 4
4 4 4
(a) 12x y z (b) 8x y z (c) 12x y z (d) 8x y z
2
2
4 3
3 2
4. The volume of a rectangular box with length l m , breadth m n and height l n is:
6 6
8
6 6
6
5 5
6
5 5
8
(a) l m n (b) l m n (c) l m n (d) l m n
8 8
9
5. The product of 2x y ¥ 4z ¥ 0 is equal to:
8 8 9
8 8 9
(a) 8x y z (b) 0 (c) 4x y z (d) 8
1 2 1
6. If x– = 3, then the value of x + is:
x x 2
(a) 7 (b) 9 (c) 5 (d) 11
2
2
7. If xy = 6 and x + y = 5 then the value of x + y is:
(a) 13 (b) 11 (c) 16 (d) 12
solve Mentally
True or False
1. A constant factor is called a numerical factor and a variable factor is called literal factor.
2
2. (p + q)(p – q) = p + q 2
3. The product of two factors with same sign is positive and with different sign is negative.
4. In addition or subtraction of algebraic expressions, unlike terms are grouped and the sum or difference
of each group is found out.
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