Q6 of 59 Page 38

Use the identity (a – b)2 = a2 – 2ab + b2 to compute:

(i) (x – 6)2 (ii) (3x – 5y)2


(iii) (5a – 4b)2 (iv) (p2 + q2)2

Given identity

(a – b)2 = a2 – 2ab + b2


(i) (x – 6)2


Using the given identity


Here a = x, b = 6


= x2 – 2× x × 6 +62


= x2 –12x +36


(ii)(3x – 5y)2


Using the given identity


Here a = 3x, b = 5y


= (3x)2 – 2× 3x × 5y + (5y)2


= 9x2 – 30xy +25y2


(iii)(5a – 4b)2


Using the given identity


Here a = 5a, b = 4b


= (5a)2 –2× 5a × 4b + (4b)2


= 25a2 – 40 ab + 16b2


(iv) (p2 – q2)2


Using the given identity


Here a = p2, b = q2


= (p2)2 – 2 × p2 × q2 + (q2)2


= p4 – 2 p2 q2 + q4


More from this chapter

All 59 →
4

Using the identity (a +b)2 = a2 + 2ab + b2, simplify the following:

(i) (a + 6)2 (ii) (3x + 2y)2


(iii) (2p + 3q)2 (iv) (x2 + 5)2

 5

Evaluate using the identity (a + b)2 = a2 + 2ab + b2

(i) (34)2 (ii) (10.2)2


(iii) (53)2 (iv) (41)2

 7

Evaluate using the identity (a – b)2 = a2 – 2ab + b2

(i) (49)2 (ii) (9.8)2


(iii) (59)2 (iv) (198)2

 8

Use the identity (a + b)(a – b) = a2 – b2 to find the products:

(i) (x – 6) (x + 6)


(ii) (3x + 5)(3x + 5)


(iii) (2a + 4b)(2a – 4b)


(iv)