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Expand the following squares, using suitable identities.

(i) (2x + 5)2

(ii) (b – 7)2

(iii) (mn + 3p)2

(iv) (xyz – 1)2

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(i) (2x + 5)2

Comparing (2x + 5)2 with (a + b)2 we have a = 2x and b = 5

a = 2x and b = 5,

(a + b)2 = a2 + 2ab + b2

(2x + 5)2 = (2x)2 + 2(2x) (5) + 52 

= 22 x2 + 20x + 25

= 22 x2 + 20x + 25

(2x + 5)2 = 4x2 + 20x + 25

(ii) (b – 7)2

Comparing (b – 7)2 with (a – b)2 we have a = b and b = 7

(a – b)2 = a2 – 2ab + b2

(b – 7)2 = b2 – 2(b) (7) + 72

(b – 7)2 = b2 – 14b + 49

(iii) (mn + 3p)2

Comparing (mn + 3p)2 with (a + b)2 we have

(a + b)2 = a2 + 2ab + b2

(mn + 3p)2 = (mn)2 + 2(mn) (3p) + (3p)2

(mn + 3p)2 = m2 n2 + 6mnp + 9p2

(iv) (xyz – 1)2

Comparing (xyz – 1)2 with (a – b)2 we have 

= a + xyz and b = 1

a = xyz and b = 1

(a – b)2 = a2 – 2ab + b2

(xyz – 1)2 = (xyz)2 – 2(xyz) (1) + 12

(xyz - 1)2 = x2 y2 z2 – 2xyz + 1

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