Q14 of 38 Page 10

Let’s express following the expressions as sum of two squares:

i.


ii.


iii.


Formulas used:


(a + b)2 = a2 + 2ab + b2 [1]


(a – b)2 = a2 – 2ab + b2 [2]


i. 2(a2 + b)2


= 2a2 + 2b2


= a2 + b2 + a2 + b2


= a2 + 2ab + b2 + a2 – 2ab + b2


Using identities [1] and [2],


= (a + b)2 + (a – b)2


ii. 50x2 + 18y2


= 25x2 + 25x2 + 9y2 + 9y2


= 25x2 + 9y2 + 25x2 + 9y2


= (5x)2 + (3y)2 + (5x)2 + (3y)2


Using identities [1] and [2],


Here, a = 5x, b = 3y


= (5x)2 + 2(5x)(3y) + (3y)2 + (5x)2 – 2(5x)(3x) + (3x)2


= (5x + 3y)2 + (5x – 3y)2


iii. a2 + b2 + c2 + d2 + 2(ac – bd)


= a2 + b2 + c2 + d2 + 2ac – 2bd


Using identities [1] and [2],


= a2 + 2ac + c2 + b2 – 2bd + d2


= (a + c)2 + (b – d)2


More from this chapter

All 38 →
12

Let’s find the product by formulae;

i.


ii.


iii.


iv.


v.


13

(a) If let’s show that and

(b) If let’s show that


(c) If let’s show that


i.


ii.


(d) If let’s show that (using formula)


(e) If then let’s find out the value of


15

i. Let’s write for which value of t, will be a whole square form.

ii. Let’s write the expression which when added to gives a whole square.


iii. If a and b are positive integers and lets write the value of a & b.


iv. an identity or an equation? Write with reason.


v. For each positive or negative value of x and y except zero the value of is always (positive or negative)


 16

Let’s solve:

i.


ii.


iii.


iv.


v.


vi.