Page 45 - Concepts of Reasoning-8

Worksheet-7.2

Using Identities

1. Find the missing steps :
2
a. x + 16x + 64
2
2
2
2
2
Observe that x + 16x + 64 are of the form a + 2ab + b where a = _____ , b = _____ , 2ab = _____
, 12m = _____
2
x + 16x + 64
=
= (x + 8) 2
2
b. 4p + 72pq + 81q 2
2
2
2
2
Observe that 4p + 36pq + 81q are of the form where a = _____ , b = _____ , 2ab = _____ =
_____
2
4p + 36pq + 81q 2
2
= (2p) + 2 × 2p × 9q + (9q) 2
=
2
c. 9y – 30yz + 25z 2
2
2
2
2
Observe that 9y – 30yz + 25z are of the form where a = 3p, b = 5z, 2ab = _____ =
2
9y – 30yz + 25z 2
=
2
d. 16p – 121q 2
2
2
2
2
2
2
Comparing 16p – 121q with a – b you can see that a = ____, b = . Using a – b = (a + b) (a – b).
2
16p – 121q 2
=
= (4p + 11q) (4p – 11q)
2. Prove the following problems by writing which identity is used to solve them :
2
2
a. The factors of m + 14m + 49 are (m + 7) .
2
2
2
b. The factors of 9p + 24pq + 16q are (3p + 4q) .
2
2
c. The factors of d – 10d + 25 are (d – 5) .
2
2
d. The factors of 9p – 121q are (3p + 11q) (3p – 11q).
3. Match the following algebraic expressions with their factors :
2
2
2
2
2
a. m + 8m + 16 i. 6 (2m + n ) (2m – n )
2
b. m – 14m + 49 ii. (m+4) 2
2
2
c. 36m – 60mm + 25n iii. (m – 7) 2
4
4
d. 24m – 6n iv. (6m – 5n) 2
45 Reasoning - 8