Page 42 - Concepts of Reasoning-8

Worksheet-6.3

Standard Identities

1. Find the following products without actual multiplication by using the suitable identities.
Also mention the identity that is being used :

a. (x + 5) (x – 3) = _______________ ; Identity : _______________
b. (2x + 6y) (2x – 6y) = _______________ ; Identity : _______________

c. (9 – 2r) (9 – 2r) = _______________ ; Identity : _______________
d. (8a + 5b) (8a + 5b) = _______________ ; Identity : _______________

e. t + k k – t = _______________ ; Identity : _______________
2 4 4 2
2. Find the values of the letter A, B and C in the following problems :
2
2
a. (5x + 2y) = (5x) + 2 (5x) (2y) – (2y) 2
2
= 5x +20xy – 2y 2
2
b. (9z + 7k) (7k – 9z) = (9z) – (7k) 2
81z – 7k 2
2
c. (t + 10) (t – 5) = t + (10 + 5)t + 10 × 5
2
= t + 15t + 50
a b 2 a 2 a b b 2
d. – = –2 –
2 2 2 2 2 2
a 2 b 2
= – ab –
2 2
2
2
2
e. 25l –9k = (5l) – (9k) 2
(5l + 9k) (5l – 9k)
3. Solve the following problems using the suitable standard identities :
2
a. Find the value of (150) without actual multiplication.
___________________________________________________________________________

b. Find the value of 58 × 62 without actual multiplication.
___________________________________________________________________________
1 2 1
c. If x + = 10, then what is the value of x + ?
2
x x
___________________________________________________________________________
1 2 1
d. If g – = 15, then what is the value of g + ?
g g 2
___________________________________________________________________________
2
2
e. If p – q = 20 and pq = 16 then find the value of p + q .
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42 Reasoning - 8